Question

The LCM of 36, 45, 465 and 310 is:

• A. 5580
• B. 5497
• C. 5560
• D. 5658

Answer 1

Answer:

A. 5580

Find the LCM of 36, 45, 465, 310.

Prime factorization

• $(36 = 2^2 \times 3^2)$

• $(45 = 3^2 \times 5)$

• $(465 = 3 \times 5 \times 31)$

• $(310 = 2 \times 5 \times 31)$

  Take highest powers of each prime

• $(2^2) (from 36)$

• $(3^2) (from 36 or 45)$

• $(5) (common highest)$

• $(31) (from 465 or 310)$

  Multiply

$\text{LCM} = 2^2 \times 3^2 \times 5 \times 31$
$= 4 \times 9 \times 5 \times 31$
$= 36 \times 5 \times 31$
$= 180 \times 31$
$= 5580$
But check carefully:
$465 has only one 3 → but 36 and 45 already give (3^2), so correct.$

Final Answer

LCM = 5580