Least Common Multiple of 40 and 48

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 40 and 48 the smallest integer that is 240 that is divisible by both numbers.

Least Common Multiple (LCM) of 40 and 48 is 240.

LCM(40,48) = 240

LCM of 40 and 48

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

LCM of:
and

Least Common Multiple of 40 and 48

LCM of 40 and 48 is 240

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 48. First we will calculate the prime factors of 40 and 48.

Prime Factorization of 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 48.

LCM(40,48) = 24×31×51
LCM(40,48) = 240

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

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

Least Common Multiple of 40 and 48 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 48, than apply into the LCM equation.

GCF(40,48) = 8
LCM(40,48) = ( 40 × 48) / 8
LCM(40,48) = 1920 / 8
LCM(40,48) = 240

Properties of LCM 40 and 48

(i) The LCM of 48 and 40 is associative

LCM of 40 and 48 = LCM of 48 and 40

Related Least Common Multiples of 40

Related Least Common Multiples of 48

Frequently Asked Questions on LCM of 40 and 48

1. What is the LCM of 40 and 48?

Answer: LCM of 40 and 48 is 240.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

3. 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.

4. How to Find the LCM of 40 and 48?

Answer:

Least Common Multiple of 40 and 48 = 240

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 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 = 240 = 2 x 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 40 and 48 is 240.