Least Common Multiple of 2142 and 2149

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2142 and 2149 the smallest integer that is 657594 that is divisible by both numbers.

Least Common Multiple (LCM) of 2142 and 2149 is 657594.

LCM(2142,2149) = 657594

LCM of 2142 and 2149

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

LCM of:
and

Least Common Multiple of 2142 and 2149

LCM of 2142 and 2149 is 657594

Least common multiple can be found by multiplying the highest exponent prime factors of 2142 and 2149. First we will calculate the prime factors of 2142 and 2149.

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

Prime Factorization of 2149


7 2149
307 307
1

Prime factors of 2149 are 7,307. Prime factorization of 2149 in exponential form is:

2149 = 71×3071

Now multiplying the highest exponent prime factors to calculate the LCM of 2142 and 2149.

LCM(2142,2149) = 21×32×71×171×3071
LCM(2142,2149) = 657594

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

Factors of 2149

List of positive integer factors of 2149 that divides 2149 without a remainder.

1, 7, 307, 2149

Least Common Multiple of 2142 and 2149 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2142 and 2149, than apply into the LCM equation.

GCF(2142,2149) = 7
LCM(2142,2149) = ( 2142 × 2149) / 7
LCM(2142,2149) = 4603158 / 7
LCM(2142,2149) = 657594

Properties of LCM 2142 and 2149

(i) The LCM of 2149 and 2142 is associative

LCM of 2142 and 2149 = LCM of 2149 and 2142

Related Least Common Multiples of 2142

Related Least Common Multiples of 2149

Frequently Asked Questions on LCM of 2142 and 2149

1. What is the LCM of 2142 and 2149?

Answer: LCM of 2142 and 2149 is 657594.

2. 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.

3. What are the Factors of 2149?

Answer: Factors of 2149 are 1, 7, 307, 2149. There are 4 integers that are factors of 2149. The greatest factor of 2149 is 2149.

4. How to Find the LCM of 2142 and 2149?

Answer:

Least Common Multiple of 2142 and 2149 = 657594

Step 1: Find the prime factorization of 2142

2142 = 2 x 3 x 3 x 7 x 17

Step 2: Find the prime factorization of 2149

2149 = 7 x 307

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

LCM = 657594 = 2 x 3 x 3 x 7 x 17 x 307

Step 4: Therefore, the least common multiple of 2142 and 2149 is 657594.