Least Common Multiple of 2138 and 2142

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2138 and 2142 the smallest integer that is 2289798 that is divisible by both numbers.

Least Common Multiple (LCM) of 2138 and 2142 is 2289798.

LCM(2138,2142) = 2289798

LCM of 2138 and 2142

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

LCM of:
and

Least Common Multiple of 2138 and 2142

LCM of 2138 and 2142 is 2289798

Least common multiple can be found by multiplying the highest exponent prime factors of 2138 and 2142. First we will calculate the prime factors of 2138 and 2142.

Prime Factorization of 2138


2 2138
1069 1069
1

Prime factors of 2138 are 2,1069. Prime factorization of 2138 in exponential form is:

2138 = 21×10691

Prime Factorization of 2142


2 2142
3 1071
3 357
7 119
17 17
1

Prime factors of 2142 are 2, 3, 7,17. Prime factorization of 2142 in exponential form is:

2142 = 21×32×71×171

Now multiplying the highest exponent prime factors to calculate the LCM of 2138 and 2142.

LCM(2138,2142) = 21×32×71×171×10691
LCM(2138,2142) = 2289798

Factors of 2138

List of positive integer factors of 2138 that divides 2138 without a remainder.

1, 2, 1069, 2138

Factors of 2142

List of positive integer factors of 2142 that divides 2142 without a remainder.

1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142

Least Common Multiple of 2138 and 2142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2138 and 2142, than apply into the LCM equation.

GCF(2138,2142) = 2
LCM(2138,2142) = ( 2138 × 2142) / 2
LCM(2138,2142) = 4579596 / 2
LCM(2138,2142) = 2289798

Properties of LCM 2138 and 2142

(i) The LCM of 2142 and 2138 is associative

LCM of 2138 and 2142 = LCM of 2142 and 2138

Related Least Common Multiples of 2138

Related Least Common Multiples of 2142

Frequently Asked Questions on LCM of 2138 and 2142

1. What is the LCM of 2138 and 2142?

Answer: LCM of 2138 and 2142 is 2289798.

2. What are the Factors of 2138?

Answer: Factors of 2138 are 1, 2, 1069, 2138. There are 4 integers that are factors of 2138. The greatest factor of 2138 is 2138.

3. What are the Factors of 2142?

Answer: Factors of 2142 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142. There are 24 integers that are factors of 2142. The greatest factor of 2142 is 2142.

4. How to Find the LCM of 2138 and 2142?

Answer:

Least Common Multiple of 2138 and 2142 = 2289798

Step 1: Find the prime factorization of 2138

2138 = 2 x 1069

Step 2: Find the prime factorization of 2142

2142 = 2 x 3 x 3 x 7 x 17

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

LCM = 2289798 = 2 x 3 x 3 x 7 x 17 x 1069

Step 4: Therefore, the least common multiple of 2138 and 2142 is 2289798.