Question

find the least common multiple (lcm) of 15 and 9.

Explanation:

Step1: Prime Factorization

Factorize 15 and 9 into primes.
$15 = 3 \times 5$
$9 = 3 \times 3$

Step2: Identify Max Exponents

For each prime (3, 5), take the highest power.

• Prime 3: max exponent is 2 (from 9: $3^2$)
• Prime 5: max exponent is 1 (from 15: $5^1$)

Step3: Calculate LCM

Multiply these highest powers:
$LCM = 3^2 \times 5 = 9 \times 5 = 45$

Answer:

45