What is the least common multiple of 15 and 20? — ACT

What is the least common multiple of $15$ and $20$ ?

Answer: 60

The least common multiple of

15

and

20

60

The correct answer is

60

. The least common multiple is the smallest positive integer that is divisible by both

15

and

20

. By listing multiples or using prime factorization (

2^2 \times 3 \times 5

), we arrive at

60

Find the prime factorization of

15

and

20

15 = 3 \times 5

and

20 = 2^2 \times 5

Decomposing numbers into their prime factors makes it straightforward to compute their least common multiple.

Identify the highest exponent for each prime factor appearing in the prime factorizations.

The prime factors present are

2

3

, and

5

. The highest powers are

2^2

3^1

, and

5^1

The least common multiple must contain all prime factors of both numbers at their maximum frequency to be divisible by both.

Calculate the product of these highest powers of the prime factors.

2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60

Multiplying these factors yields the smallest positive integer that is a multiple of both original numbers.

Least Common Multiple (LCM)

Estimated Time:45s

Question