Question

Work out the lowest common multiple (LCM) of 270 and 450

Answer 1

1350

Explanation:

Find the prime factors of both numbers:

• 270 = 2 × 3 × 3 × 3 × 5

• 450 = 2 × 3 × 3 × 5 × 5

For each prime factor, identify when it occurs the most as a factor within the prime factorizations:

• The highest number of times the prime factor 2 occurs is once (in both numbers).
• The highest number of times the prime factor 3 occurs is three times (in the number 270).
• The highest number of times the prime factor 5 occurs is twice (in the number 450).

Multiply these factors together to find the LCM:

⇒ 2 × 3 × 3 × 3 × 5 × 5 = 1350

Therefore, the lowest common multiple of 270 and 450 is 1350.