Least Common Multiple of 10114 and 10120

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10114 and 10120 the smallest integer that is 51176840 that is divisible by both numbers.

Least Common Multiple (LCM) of 10114 and 10120 is 51176840.

LCM(10114,10120) = 51176840

LCM of 10114 and 10120

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

LCM of:
and

Least Common Multiple of 10114 and 10120

LCM of 10114 and 10120 is 51176840

Least common multiple can be found by multiplying the highest exponent prime factors of 10114 and 10120. First we will calculate the prime factors of 10114 and 10120.

Prime Factorization of 10114


2 10114
13 5057
389 389
1

Prime factors of 10114 are 2, 13,389. Prime factorization of 10114 in exponential form is:

10114 = 21×131×3891

Prime Factorization of 10120


2 10120
2 5060
2 2530
5 1265
11 253
23 23
1

Prime factors of 10120 are 2, 5, 11,23. Prime factorization of 10120 in exponential form is:

10120 = 23×51×111×231

Now multiplying the highest exponent prime factors to calculate the LCM of 10114 and 10120.

LCM(10114,10120) = 23×51×111×131×231×3891
LCM(10114,10120) = 51176840

Factors of 10114

List of positive integer factors of 10114 that divides 10114 without a remainder.

1, 2, 13, 26, 389, 778, 5057, 10114

Factors of 10120

List of positive integer factors of 10120 that divides 10120 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 23, 40, 44, 46, 55, 88, 92, 110, 115, 184, 220, 230, 253, 440, 460, 506, 920, 1012, 1265, 2024, 2530, 5060, 10120

Least Common Multiple of 10114 and 10120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10114 and 10120, than apply into the LCM equation.

GCF(10114,10120) = 2
LCM(10114,10120) = ( 10114 × 10120) / 2
LCM(10114,10120) = 102353680 / 2
LCM(10114,10120) = 51176840

Properties of LCM 10114 and 10120

(i) The LCM of 10120 and 10114 is associative

LCM of 10114 and 10120 = LCM of 10120 and 10114

Related Least Common Multiples of 10114

Related Least Common Multiples of 10120

Frequently Asked Questions on LCM of 10114 and 10120

1. What is the LCM of 10114 and 10120?

Answer: LCM of 10114 and 10120 is 51176840.

2. What are the Factors of 10114?

Answer: Factors of 10114 are 1, 2, 13, 26, 389, 778, 5057, 10114. There are 8 integers that are factors of 10114. The greatest factor of 10114 is 10114.

3. What are the Factors of 10120?

Answer: Factors of 10120 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 23, 40, 44, 46, 55, 88, 92, 110, 115, 184, 220, 230, 253, 440, 460, 506, 920, 1012, 1265, 2024, 2530, 5060, 10120. There are 32 integers that are factors of 10120. The greatest factor of 10120 is 10120.

4. How to Find the LCM of 10114 and 10120?

Answer:

Least Common Multiple of 10114 and 10120 = 51176840

Step 1: Find the prime factorization of 10114

10114 = 2 x 13 x 389

Step 2: Find the prime factorization of 10120

10120 = 2 x 2 x 2 x 5 x 11 x 23

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

LCM = 51176840 = 2 x 2 x 2 x 5 x 11 x 13 x 23 x 389

Step 4: Therefore, the least common multiple of 10114 and 10120 is 51176840.