L.C.M of 7 ,10 and 2 solve it and give me fast
The correct answer and explanation is:
Correct Answer: 70
Explanation:
The Least Common Multiple (LCM) of a group of numbers is the smallest number that all the given numbers divide without leaving a remainder.
To find the LCM of 7, 10, and 2, follow these steps:
Step 1: Prime Factorization
- 7 is a prime number: 7 = 7
- 10 can be factored as: 10 = 2 × 5
- 2 is a prime number: 2 = 2
Step 2: Identify All Prime Factors
From all the numbers, the prime factors involved are:
- 2 (from 2 and 10)
- 5 (from 10)
- 7 (from 7)
Now take the highest power of each prime number:
- Highest power of 2 is 2¹
- Highest power of 5 is 5¹
- Highest power of 7 is 7¹
Step 3: Multiply the Highest Powers
Now multiply them together to get the LCM:
2 × 5 × 7 = 70
Why This Works
The LCM must be divisible by each of the original numbers:
- 70 ÷ 7 = 10 (no remainder)
- 70 ÷ 10 = 7 (no remainder)
- 70 ÷ 2 = 35 (no remainder)
Thus, 70 is the smallest number divisible by 7, 10, and 2.
Practical Use
Finding the LCM is useful in many situations, especially when adding or comparing fractions with different denominators, or solving problems involving repeated events or cycles. In programming, engineering, and real-life tasks such as scheduling or machine operations, LCM helps in finding common time intervals or shared working periods.
In conclusion, the LCM of 7, 10, and 2 is 70.