Least Common Multiple of 837 and 840

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 837 and 840 the smallest integer that is 234360 that is divisible by both numbers.

Least Common Multiple (LCM) of 837 and 840 is 234360.

LCM(837,840) = 234360

LCM of 837 and 840

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

LCM of:
and

Least Common Multiple of 837 and 840

LCM of 837 and 840 is 234360

Least common multiple can be found by multiplying the highest exponent prime factors of 837 and 840. First we will calculate the prime factors of 837 and 840.

Prime Factorization of 837


3 837
3 279
3 93
31 31
1

Prime factors of 837 are 3,31. Prime factorization of 837 in exponential form is:

837 = 33×311

Prime Factorization of 840


2 840
2 420
2 210
3 105
5 35
7 7
1

Prime factors of 840 are 2, 3, 5,7. Prime factorization of 840 in exponential form is:

840 = 23×31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 837 and 840.

LCM(837,840) = 23×33×51×71×311
LCM(837,840) = 234360

Factors of 837

List of positive integer factors of 837 that divides 837 without a remainder.

1, 3, 9, 27, 31, 93, 279, 837

Factors of 840

List of positive integer factors of 840 that divides 840 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840

Least Common Multiple of 837 and 840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 837 and 840, than apply into the LCM equation.

GCF(837,840) = 3
LCM(837,840) = ( 837 × 840) / 3
LCM(837,840) = 703080 / 3
LCM(837,840) = 234360

Properties of LCM 837 and 840

(i) The LCM of 840 and 837 is associative

LCM of 837 and 840 = LCM of 840 and 837

Related Least Common Multiples of 837

Related Least Common Multiples of 840

Frequently Asked Questions on LCM of 837 and 840

1. What is the LCM of 837 and 840?

Answer: LCM of 837 and 840 is 234360.

2. What are the Factors of 837?

Answer: Factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837. There are 8 integers that are factors of 837. The greatest factor of 837 is 837.

3. What are the Factors of 840?

Answer: Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. There are 32 integers that are factors of 840. The greatest factor of 840 is 840.

4. How to Find the LCM of 837 and 840?

Answer:

Least Common Multiple of 837 and 840 = 234360

Step 1: Find the prime factorization of 837

837 = 3 x 3 x 3 x 31

Step 2: Find the prime factorization of 840

840 = 2 x 2 x 2 x 3 x 5 x 7

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

LCM = 234360 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 31

Step 4: Therefore, the least common multiple of 837 and 840 is 234360.