Question

Find the lowest common multiple (LCM) of 36 and 48. Note: Please make your final answer clear by writing LCM = ...

Answer 1

The lowest common multiple (LCM) of 36 and 48 is found by taking the highest powers of their prime factors, resulting in a LCM of 144.

Step-by-step explanation:

To find the lowest common multiple (LCM) of 36 and 48, we first need to find the prime factors of each number.

For 36, the prime factorization is 22 × 32.

For 48, the prime factorization is 24 × 31.

To get the LCM, we take the highest power of each prime number involved in the factorizations:

• For 2, the highest power is 24.
• For 3, the highest power is 32.

Multiplying these together gives us:

LCM = 24 × 32 = 16 × 9 = 144.

So, the LCM of 36 and 48 is 144.