{"id":16718,"date":"2025-06-11T19:30:38","date_gmt":"2025-06-11T19:30:38","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=16718"},"modified":"2025-06-11T19:30:42","modified_gmt":"2025-06-11T19:30:42","slug":"every-6th-customer-at-the-flower-shop-receives-a-free-rose-and-every-9th-customer-receives-a-free-lily","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/every-6th-customer-at-the-flower-shop-receives-a-free-rose-and-every-9th-customer-receives-a-free-lily\/","title":{"rendered":"Every 6th customer at the flower shop receives a free rose, and every 9th customer receives a free lily"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Every 6th customer at the flower shop receives a free rose, and every 9th customer receives a free lily. Which customer will be the first to receive a free rose and a free lily?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Correct Answer: 18th customer<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This is a classic <strong>least common multiple (LCM)<\/strong> problem, often seen in math questions involving repeating patterns or schedules.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The problem states:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every <strong>6th customer<\/strong> gets a <strong>free rose<\/strong>.<\/li>\n\n\n\n<li>Every <strong>9th customer<\/strong> gets a <strong>free lily<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We are asked to find the <strong>first customer who receives both a rose and a lily<\/strong>. This customer must be both a multiple of 6 <strong>and<\/strong> a multiple of 9.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this, we need to find the <strong>Least Common Multiple (LCM)<\/strong> of 6 and 9.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: Prime factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 = 2 \u00d7 3<\/li>\n\n\n\n<li>9 = 3 \u00d7 3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: Take the highest power of each prime<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2\u00b9 (from 6)<\/li>\n\n\n\n<li>3\u00b2 (from 9)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Now multiply these together:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>LCM = 2\u00b9 \u00d7 3\u00b2 = 2 \u00d7 9 = <strong>18<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">So, the <strong>18th customer<\/strong> is the first person to receive <strong>both<\/strong> a free rose and a free lily.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Why LCM Works Here:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The LCM of two numbers is the smallest number that both original numbers divide into evenly. In this case:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every 6th customer = 6, 12, 18, 24, \u2026<\/li>\n\n\n\n<li>Every 9th customer = 9, 18, 27, 36, \u2026<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The first number common to both lists is <strong>18<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Real-World Meaning:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you work at or manage a flower shop, understanding patterns like this helps with planning promotions or inventory. For example, by the time you&#8217;ve served 18 customers, you should have at least <strong>one rose and one lily<\/strong> ready for the lucky customer who qualifies for both freebies.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the <strong>18th customer<\/strong> will be the <strong>first to receive both<\/strong> a free rose <strong>and<\/strong> a free lily.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Every 6th customer at the flower shop receives a free rose, and every 9th customer receives a free lily. Which customer will be the first to receive a free rose and a free lily? The correct answer and explanation is: Correct Answer: 18th customer Explanation (300 words): This is a classic least common multiple (LCM) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-16718","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16718","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=16718"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16718\/revisions"}],"predecessor-version":[{"id":16719,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16718\/revisions\/16719"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16718"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16718"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16718"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}