Question

the lcm of 24,36,and 40 is

Answer 1

LCM of 24, 36 and 40 is 360

_____________________

24 = 2 × 3 × 2 × 2

36 = 2 × 3 × 3 × 2

40 = 2 × 2 × 2 × 5

LCM of (24, 36, 40) =2 × 3 × 2 × 2 × 3 × 5

Answer 2

Given: The numbers are$24,36,\ and\ 40$.

We have to find the LCM of the above numbers.

We are solving in the following way:

We have,

The numbers are$24,36,\ and\ 40$.

First, we will list all prime factors for each number.

Prime Factorization of 24 is:

$2 \times 2 \times 2 \times 3 => 2^3 \times 3^1$

Prime Factorization of 36 is:

$2 \times 2 \times 3 \times 3 => 2^2 \times3^2$

Prime Factorization of 40 is:

$2 \times 2 \times 2 \times 5 => 2^3 \times5^1$

For each prime factor, we will find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

$2, 2, 2, 3, 3, 5$

Multiplying these factors together to find the LCM.

$LCM = 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 360$

In exponential form:

$LCM = 2^3 \times 3^2 \times 5^1 = 360LCM = 360$

Therefore,

$LCM(24, 36, 40) = 360$

Hence, we get$LCM=360$.