Question

What is the least common multiple (LCM) of the numbers 90, 60, 75, and 35?

• A. 2700
• B. 6300
• C. 4250
• D. 2750

Hint:

To find the LCM, take the highest power of all prime factors that appear in the numbers.

Answer 1

The Correct Option is B

We find the prime factorization of each number: - 90 = \( 2^1 \times 3^2 \times 5^1 \) - 60 = \( 2^2 \times 3^1 \times 5^1 \) - 75 = \( 3^1 \times 5^2 \) - 35 = \( 5^1 \times 7^1 \) Taking the highest powers of all prime factors: \[ \text{LCM} = 2^2 \times 3^2 \times 5^2 \times 7^1 \] \[ = 4 \times 9 \times 25 \times 7 \] Step-by-step multiplication: \[ 4 \times 9 = 36 \] \[ 36 \times 25 = 900 \] \[ 900 \times 7 = 6300 \]
Thus, the LCM is 6300.