Find the least common multiple of 154 and 231.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Correct Answer: 3,542<\/strong><\/p>\n\n\n\n To find the least common multiple (LCM) of 154 and 231, begin with their prime factorizations.<\/p>\n\n\n\n 154<\/strong> 231<\/strong> The prime factors for 154 are 2, 7, and 11 To find the least common multiple, take each prime factor that appears<\/strong> in either number and use the highest power<\/strong> of each.<\/p>\n\n\n\n Multiply all the prime factors: First: However, this is not correct for the LCM because 462 is a common factor, but not the least common multiple<\/em>. Let’s go step-by-step using the correct method.<\/p>\n\n\n\n The formula for LCM is: First, find the greatest common factor (GCF) of 154 and 231.<\/p>\n\n\n\n From the factorizations: The common prime factors are 7<\/strong> and 11<\/strong>, so: Now use the LCM formula: First: Then divide by 77: So the LCM is 462<\/strong><\/p>\n\n\n\n The earlier answer was wrong. Correct LCM is 462<\/strong>, not 3,542. Find the least common multiple of 154 and 231. The correct answer and explanation is: Correct Answer: 3,542 To find the least common multiple (LCM) of 154 and 231, begin with their prime factorizations. Step 1: Prime factorization 154Divide by 2:154 \u00f7 2 = 7777 \u00f7 7 = 1111 is a prime numberSo, the prime […]<\/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-34306","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34306","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=34306"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34306\/revisions"}],"predecessor-version":[{"id":34311,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34306\/revisions\/34311"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Prime factorization<\/h3>\n\n\n\n
Divide by 2:
154 \u00f7 2 = 77
77 \u00f7 7 = 11
11 is a prime number
So, the prime factorization of 154 is:
2 \u00d7 7 \u00d7 11<\/strong><\/p>\n\n\n\n
Divide by 3:
231 \u00f7 3 = 77
77 \u00f7 7 = 11
11 is a prime number
So, the prime factorization of 231 is:
3 \u00d7 7 \u00d7 11<\/strong><\/p>\n\n\n\nStep 2: Identify all prime factors<\/h3>\n\n\n\n
The prime factors for 231 are 3, 7, and 11<\/p>\n\n\n\n\n
2 \u00d7 3 \u00d7 7 \u00d7 11<\/strong><\/p>\n\n\n\n
2 \u00d7 3 = 6
6 \u00d7 7 = 42
42 \u00d7 11 = 462<\/strong><\/p>\n\n\n\nStep 3: Use the formula<\/h3>\n\n\n\n
LCM(a, b) = (a \u00d7 b) \u00f7 GCF(a, b)<\/strong><\/p>\n\n\n\n
154 = 2 \u00d7 7 \u00d7 11
231 = 3 \u00d7 7 \u00d7 11<\/p>\n\n\n\n
GCF = 7 \u00d7 11 = 77<\/strong><\/p>\n\n\n\n
LCM = (154 \u00d7 231) \u00f7 77<\/strong><\/p>\n\n\n\n
154 \u00d7 231 = 35,574<\/p>\n\n\n\n
35,574 \u00f7 77 = 462<\/strong><\/p>\n\n\n\n
Explanation: The LCM is the smallest number that is a multiple of both 154 and 231. Using prime factorizations and the formula helps find the accurate result.<\/p>\n","protected":false},"excerpt":{"rendered":"