Least Common Multiple of 48 and 18

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 48 and 18 the smallest integer that is 144 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 18 is 144.

LCM(48,18) = 144

LCM of 48 and 18

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 48 and 18

LCM of 48 and 18 is 144

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 18. First we will calculate the prime factors of 48 and 18.

Prime Factorization of 48


2 48
2 24
2 12
2 6
3 3
1

Prime factors of 48 are 2,3. Prime factorization of 48 in exponential form is:

48 = 24×31

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 18.

LCM(48,18) = 24×32
LCM(48,18) = 144

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Least Common Multiple of 48 and 18 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 18, than apply into the LCM equation.

GCF(48,18) = 6
LCM(48,18) = ( 48 × 18) / 6
LCM(48,18) = 864 / 6
LCM(48,18) = 144

Properties of LCM 48 and 18

(i) The LCM of 18 and 48 is associative

LCM of 48 and 18 = LCM of 18 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 18

Frequently Asked Questions on LCM of 48 and 18

1. What is the LCM of 48 and 18?

Answer: LCM of 48 and 18 is 144.

2. What are the Factors of 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

3. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the LCM of 48 and 18?

Answer:

Least Common Multiple of 48 and 18 = 144

Step 1: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 18

18 = 2 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 144 = 2 x 2 x 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 48 and 18 is 144.