Least Common Multiple of 2142 and 2144

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 2144 the smallest integer that is 2296224 that is divisible by both numbers.

Least Common Multiple (LCM) of 2142 and 2144 is 2296224.

LCM(2142,2144) = 2296224

LCM of 2142 and 2144

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

LCM of:
and

Least Common Multiple of 2142 and 2144

LCM of 2142 and 2144 is 2296224

Least common multiple can be found by multiplying the highest exponent prime factors of 2142 and 2144. First we will calculate the prime factors of 2142 and 2144.

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 2144


2 2144
2 1072
2 536
2 268
2 134
67 67
1

Prime factors of 2144 are 2,67. Prime factorization of 2144 in exponential form is:

2144 = 25×671

Now multiplying the highest exponent prime factors to calculate the LCM of 2142 and 2144.

LCM(2142,2144) = 25×32×71×171×671
LCM(2142,2144) = 2296224

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 2144

List of positive integer factors of 2144 that divides 2144 without a remainder.

1, 2, 4, 8, 16, 32, 67, 134, 268, 536, 1072, 2144

Least Common Multiple of 2142 and 2144 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 2144, than apply into the LCM equation.

GCF(2142,2144) = 2
LCM(2142,2144) = ( 2142 × 2144) / 2
LCM(2142,2144) = 4592448 / 2
LCM(2142,2144) = 2296224

Properties of LCM 2142 and 2144

(i) The LCM of 2144 and 2142 is associative

LCM of 2142 and 2144 = LCM of 2144 and 2142

Related Least Common Multiples of 2142

Related Least Common Multiples of 2144

Frequently Asked Questions on LCM of 2142 and 2144

1. What is the LCM of 2142 and 2144?

Answer: LCM of 2142 and 2144 is 2296224.

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 2144?

Answer: Factors of 2144 are 1, 2, 4, 8, 16, 32, 67, 134, 268, 536, 1072, 2144. There are 12 integers that are factors of 2144. The greatest factor of 2144 is 2144.

4. How to Find the LCM of 2142 and 2144?

Answer:

Least Common Multiple of 2142 and 2144 = 2296224

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 2144

2144 = 2 x 2 x 2 x 2 x 2 x 67

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

LCM = 2296224 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 17 x 67

Step 4: Therefore, the least common multiple of 2142 and 2144 is 2296224.