Least Common Multiple of 64 and 67

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 64 and 67 the smallest integer that is 4288 that is divisible by both numbers.

Least Common Multiple (LCM) of 64 and 67 is 4288.

LCM(64,67) = 4288

LCM of 64 and 67

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

LCM of:
and

Least Common Multiple of 64 and 67

LCM of 64 and 67 is 4288

Least common multiple can be found by multiplying the highest exponent prime factors of 64 and 67. First we will calculate the prime factors of 64 and 67.

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

Prime Factorization of 67


67 67
1

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 671

Now multiplying the highest exponent prime factors to calculate the LCM of 64 and 67.

LCM(64,67) = 26×671
LCM(64,67) = 4288

Factors of 64

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

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

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1, 67

Least Common Multiple of 64 and 67 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 64 and 67, than apply into the LCM equation.

GCF(64,67) = 1
LCM(64,67) = ( 64 × 67) / 1
LCM(64,67) = 4288 / 1
LCM(64,67) = 4288

Properties of LCM 64 and 67

(i) The LCM of 67 and 64 is associative

LCM of 64 and 67 = LCM of 67 and 64

Related Least Common Multiples of 64

Related Least Common Multiples of 67

Frequently Asked Questions on LCM of 64 and 67

1. What is the LCM of 64 and 67?

Answer: LCM of 64 and 67 is 4288.

2. 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.

3. What are the Factors of 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

4. How to Find the LCM of 64 and 67?

Answer:

Least Common Multiple of 64 and 67 = 4288

Step 1: Find the prime factorization of 64

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

Step 2: Find the prime factorization of 67

67 = 67

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

LCM = 4288 = 2 x 2 x 2 x 2 x 2 x 2 x 67

Step 4: Therefore, the least common multiple of 64 and 67 is 4288.