Least Common Multiple of 10140 and 10144

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10140 and 10144 the smallest integer that is 25715040 that is divisible by both numbers.

Least Common Multiple (LCM) of 10140 and 10144 is 25715040.

LCM(10140,10144) = 25715040

LCM of 10140 and 10144

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

LCM of:
and

Least Common Multiple of 10140 and 10144

LCM of 10140 and 10144 is 25715040

Least common multiple can be found by multiplying the highest exponent prime factors of 10140 and 10144. First we will calculate the prime factors of 10140 and 10144.

Prime Factorization of 10140


2 10140
2 5070
3 2535
5 845
13 169
13 13
1

Prime factors of 10140 are 2, 3, 5,13. Prime factorization of 10140 in exponential form is:

10140 = 22×31×51×132

Prime Factorization of 10144


2 10144
2 5072
2 2536
2 1268
2 634
317 317
1

Prime factors of 10144 are 2,317. Prime factorization of 10144 in exponential form is:

10144 = 25×3171

Now multiplying the highest exponent prime factors to calculate the LCM of 10140 and 10144.

LCM(10140,10144) = 25×31×51×132×3171
LCM(10140,10144) = 25715040

Factors of 10140

List of positive integer factors of 10140 that divides 10140 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 169, 195, 260, 338, 390, 507, 676, 780, 845, 1014, 1690, 2028, 2535, 3380, 5070, 10140

Factors of 10144

List of positive integer factors of 10144 that divides 10144 without a remainder.

1, 2, 4, 8, 16, 32, 317, 634, 1268, 2536, 5072, 10144

Least Common Multiple of 10140 and 10144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10140 and 10144, than apply into the LCM equation.

GCF(10140,10144) = 4
LCM(10140,10144) = ( 10140 × 10144) / 4
LCM(10140,10144) = 102860160 / 4
LCM(10140,10144) = 25715040

Properties of LCM 10140 and 10144

(i) The LCM of 10144 and 10140 is associative

LCM of 10140 and 10144 = LCM of 10144 and 10140

Related Least Common Multiples of 10140

Related Least Common Multiples of 10144

Frequently Asked Questions on LCM of 10140 and 10144

1. What is the LCM of 10140 and 10144?

Answer: LCM of 10140 and 10144 is 25715040.

2. What are the Factors of 10140?

Answer: Factors of 10140 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 169, 195, 260, 338, 390, 507, 676, 780, 845, 1014, 1690, 2028, 2535, 3380, 5070, 10140. There are 36 integers that are factors of 10140. The greatest factor of 10140 is 10140.

3. What are the Factors of 10144?

Answer: Factors of 10144 are 1, 2, 4, 8, 16, 32, 317, 634, 1268, 2536, 5072, 10144. There are 12 integers that are factors of 10144. The greatest factor of 10144 is 10144.

4. How to Find the LCM of 10140 and 10144?

Answer:

Least Common Multiple of 10140 and 10144 = 25715040

Step 1: Find the prime factorization of 10140

10140 = 2 x 2 x 3 x 5 x 13 x 13

Step 2: Find the prime factorization of 10144

10144 = 2 x 2 x 2 x 2 x 2 x 317

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

LCM = 25715040 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 13 x 13 x 317

Step 4: Therefore, the least common multiple of 10140 and 10144 is 25715040.