Question

Find (by factoring into powers of primes):
a) LCM (8,28,10)
b) LCM (6,20)

Answer 1

To find the LCM of a set of numbers, factor each number into powers of primes and multiply the highest power of each prime. For (8, 28, 10), the LCM is 280. For (6, 20), the LCM is 60.

Step-by-step explanation:

To find the LCM (Least Common Multiple) of a set of numbers, we need to factor each number into powers of primes and then multiply the highest power of each prime.

a) For 8, 28, and 10:

• 8 = 2^3
• 28 = 2^2 * 7
• 10 = 2 * 5

The highest power of 2 is 2^3, the highest power of 7 is 7^1, and the highest power of 5 is 5^1. Therefore, LCM (8, 28, 10) = 2^3 * 7^1 * 5^1 = 280.

b) For 6 and 20:

• 6 = 2 * 3
• 20 = 2^2 * 5

The highest power of 2 is 2^2, the highest power of 3 is 3^1, and the highest power of 5 is 5^1. Therefore, LCM (6, 20) = 2^2 * 3^1 * 5^1

= 60.