What is the least common multiple of first 15 positive integers?

Question

Simran Mehta · Accepted Answer

To find the LCM, we need to consider the highest power of each prime number that appears in the factorizations of the numbers from 1 to 15.Prime Numbers within the range:
The prime numbers between 1 and 15 are: 2, 3, 5, 7, 11, and 13.Determine the highest power of each prime within the range:
2: 2^3 = 8 (since 2^4 = 16 exceeds 15)3: 3^2 = 9 (since 3^3 = 27 exceeds 15)5: 5^1 = 57: 7^1 = 711: 11^1 = 1113: 13^1 = 13LCM Calculation:
The LCM is obtained by multiplying the highest powers of all prime numbers together: LCM = 2^3 * 3^2 * 5^1 * 7^1 * 11^1 * 13^1Perform the Calculation:
2^3 = 83^2 = 95^1 = 57^1 = 711^1 = 1113^1 = 13Now, multiply these together: LCM = 8 * 9 * 5 * 7 * 11 * 13
Performing the multiplication step-by-step:
8 * 9 = 7272 * 5 = 360360 * 7 = 25202520 * 11 = 2772027720 * 13 = 360360