Least Common Multiple of 40 and 64

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 64 the smallest integer that is 320 that is divisible by both numbers.

Least Common Multiple (LCM) of 40 and 64 is 320.

LCM(40,64) = 320

LCM of 40 and 64

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

LCM of:
and

Least Common Multiple of 40 and 64

LCM of 40 and 64 is 320

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 64. First we will calculate the prime factors of 40 and 64.

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 64


2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:

64 = 26

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 64.

LCM(40,64) = 26×51
LCM(40,64) = 320

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 64

List of positive integer factors of 64 that divides 64 without a remainder.

1, 2, 4, 8, 16, 32, 64

Least Common Multiple of 40 and 64 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 64, than apply into the LCM equation.

GCF(40,64) = 8
LCM(40,64) = ( 40 × 64) / 8
LCM(40,64) = 2560 / 8
LCM(40,64) = 320

Properties of LCM 40 and 64

(i) The LCM of 64 and 40 is associative

LCM of 40 and 64 = LCM of 64 and 40

Related Least Common Multiples of 40

Related Least Common Multiples of 64

Frequently Asked Questions on LCM of 40 and 64

1. What is the LCM of 40 and 64?

Answer: LCM of 40 and 64 is 320.

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 64?

Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.

4. How to Find the LCM of 40 and 64?

Answer:

Least Common Multiple of 40 and 64 = 320

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 64

64 = 2 x 2 x 2 x 2 x 2 x 2

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

LCM = 320 = 2 x 2 x 2 x 2 x 2 x 2 x 5

Step 4: Therefore, the least common multiple of 40 and 64 is 320.