Least Common Multiple of 12 and 26

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12 and 26 the smallest integer that is 156 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 26 is 156.

LCM(12,26) = 156

LCM of 12 and 26

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

LCM of:
and

Least Common Multiple of 12 and 26

LCM of 12 and 26 is 156

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 26. First we will calculate the prime factors of 12 and 26.

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Prime Factorization of 26


2 26
13 13
1

Prime factors of 26 are 2,13. Prime factorization of 26 in exponential form is:

26 = 21×131

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 26.

LCM(12,26) = 22×31×131
LCM(12,26) = 156

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 26

List of positive integer factors of 26 that divides 26 without a remainder.

1, 2, 13, 26

Least Common Multiple of 12 and 26 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 26, than apply into the LCM equation.

GCF(12,26) = 2
LCM(12,26) = ( 12 × 26) / 2
LCM(12,26) = 312 / 2
LCM(12,26) = 156

Properties of LCM 12 and 26

(i) The LCM of 26 and 12 is associative

LCM of 12 and 26 = LCM of 26 and 12

Related Least Common Multiples of 12

Related Least Common Multiples of 26

Frequently Asked Questions on LCM of 12 and 26

1. What is the LCM of 12 and 26?

Answer: LCM of 12 and 26 is 156.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

4. How to Find the LCM of 12 and 26?

Answer:

Least Common Multiple of 12 and 26 = 156

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 26

26 = 2 x 13

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

LCM = 156 = 2 x 2 x 3 x 13

Step 4: Therefore, the least common multiple of 12 and 26 is 156.