Least Common Multiple of 48 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 48 and 64 the smallest integer that is 192 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 64 is 192.

LCM(48,64) = 192

LCM of 48 and 64

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

LCM of:
and

Least Common Multiple of 48 and 64

LCM of 48 and 64 is 192

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 64. First we will calculate the prime factors of 48 and 64.

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 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 48 and 64.

LCM(48,64) = 26×31
LCM(48,64) = 192

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 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 48 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 48 and 64, than apply into the LCM equation.

GCF(48,64) = 16
LCM(48,64) = ( 48 × 64) / 16
LCM(48,64) = 3072 / 16
LCM(48,64) = 192

Properties of LCM 48 and 64

(i) The LCM of 64 and 48 is associative

LCM of 48 and 64 = LCM of 64 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 64

Frequently Asked Questions on LCM of 48 and 64

1. What is the LCM of 48 and 64?

Answer: LCM of 48 and 64 is 192.

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 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 48 and 64?

Answer:

Least Common Multiple of 48 and 64 = 192

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 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 = 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 48 and 64 is 192.