Least Common Multiple of 7140 and 7146

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7140 and 7146 the smallest integer that is 8503740 that is divisible by both numbers.

Least Common Multiple (LCM) of 7140 and 7146 is 8503740.

LCM(7140,7146) = 8503740

LCM of 7140 and 7146

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

LCM of:
and

Least Common Multiple of 7140 and 7146

LCM of 7140 and 7146 is 8503740

Least common multiple can be found by multiplying the highest exponent prime factors of 7140 and 7146. First we will calculate the prime factors of 7140 and 7146.

Prime Factorization of 7140


2 7140
2 3570
3 1785
5 595
7 119
17 17
1

Prime factors of 7140 are 2, 3, 5, 7,17. Prime factorization of 7140 in exponential form is:

7140 = 22×31×51×71×171

Prime Factorization of 7146


2 7146
3 3573
3 1191
397 397
1

Prime factors of 7146 are 2, 3,397. Prime factorization of 7146 in exponential form is:

7146 = 21×32×3971

Now multiplying the highest exponent prime factors to calculate the LCM of 7140 and 7146.

LCM(7140,7146) = 22×32×51×71×171×3971
LCM(7140,7146) = 8503740

Factors of 7140

List of positive integer factors of 7140 that divides 7140 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140

Factors of 7146

List of positive integer factors of 7146 that divides 7146 without a remainder.

1, 2, 3, 6, 9, 18, 397, 794, 1191, 2382, 3573, 7146

Least Common Multiple of 7140 and 7146 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7140 and 7146, than apply into the LCM equation.

GCF(7140,7146) = 6
LCM(7140,7146) = ( 7140 × 7146) / 6
LCM(7140,7146) = 51022440 / 6
LCM(7140,7146) = 8503740

Properties of LCM 7140 and 7146

(i) The LCM of 7146 and 7140 is associative

LCM of 7140 and 7146 = LCM of 7146 and 7140

Related Least Common Multiples of 7140

Related Least Common Multiples of 7146

Frequently Asked Questions on LCM of 7140 and 7146

1. What is the LCM of 7140 and 7146?

Answer: LCM of 7140 and 7146 is 8503740.

2. What are the Factors of 7140?

Answer: Factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140. There are 48 integers that are factors of 7140. The greatest factor of 7140 is 7140.

3. What are the Factors of 7146?

Answer: Factors of 7146 are 1, 2, 3, 6, 9, 18, 397, 794, 1191, 2382, 3573, 7146. There are 12 integers that are factors of 7146. The greatest factor of 7146 is 7146.

4. How to Find the LCM of 7140 and 7146?

Answer:

Least Common Multiple of 7140 and 7146 = 8503740

Step 1: Find the prime factorization of 7140

7140 = 2 x 2 x 3 x 5 x 7 x 17

Step 2: Find the prime factorization of 7146

7146 = 2 x 3 x 3 x 397

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

LCM = 8503740 = 2 x 2 x 3 x 3 x 5 x 7 x 17 x 397

Step 4: Therefore, the least common multiple of 7140 and 7146 is 8503740.