Least Common Multiple of 264 and 268

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 264 and 268 the smallest integer that is 17688 that is divisible by both numbers.

Least Common Multiple (LCM) of 264 and 268 is 17688.

LCM(264,268) = 17688

LCM of 264 and 268

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

LCM of:
and

Least Common Multiple of 264 and 268

LCM of 264 and 268 is 17688

Least common multiple can be found by multiplying the highest exponent prime factors of 264 and 268. First we will calculate the prime factors of 264 and 268.

Prime Factorization of 264


2 264
2 132
2 66
3 33
11 11
1

Prime factors of 264 are 2, 3,11. Prime factorization of 264 in exponential form is:

264 = 23×31×111

Prime Factorization of 268


2 268
2 134
67 67
1

Prime factors of 268 are 2,67. Prime factorization of 268 in exponential form is:

268 = 22×671

Now multiplying the highest exponent prime factors to calculate the LCM of 264 and 268.

LCM(264,268) = 23×31×111×671
LCM(264,268) = 17688

Factors of 264

List of positive integer factors of 264 that divides 264 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264

Factors of 268

List of positive integer factors of 268 that divides 268 without a remainder.

1, 2, 4, 67, 134, 268

Least Common Multiple of 264 and 268 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 264 and 268, than apply into the LCM equation.

GCF(264,268) = 4
LCM(264,268) = ( 264 × 268) / 4
LCM(264,268) = 70752 / 4
LCM(264,268) = 17688

Properties of LCM 264 and 268

(i) The LCM of 268 and 264 is associative

LCM of 264 and 268 = LCM of 268 and 264

Related Least Common Multiples of 264

Related Least Common Multiples of 268

Frequently Asked Questions on LCM of 264 and 268

1. What is the LCM of 264 and 268?

Answer: LCM of 264 and 268 is 17688.

2. What are the Factors of 264?

Answer: Factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 integers that are factors of 264. The greatest factor of 264 is 264.

3. What are the Factors of 268?

Answer: Factors of 268 are 1, 2, 4, 67, 134, 268. There are 6 integers that are factors of 268. The greatest factor of 268 is 268.

4. How to Find the LCM of 264 and 268?

Answer:

Least Common Multiple of 264 and 268 = 17688

Step 1: Find the prime factorization of 264

264 = 2 x 2 x 2 x 3 x 11

Step 2: Find the prime factorization of 268

268 = 2 x 2 x 67

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

LCM = 17688 = 2 x 2 x 2 x 3 x 11 x 67

Step 4: Therefore, the least common multiple of 264 and 268 is 17688.