Least Common Multiple of 40 and 42

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 40 and 42 the smallest integer that is 840 that is divisible by both numbers.

Least Common Multiple (LCM) of 40 and 42 is 840.

LCM(40,42) = 840

LCM of 40 and 42

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

LCM of:
and

Least Common Multiple of 40 and 42

LCM of 40 and 42 is 840

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 42. First we will calculate the prime factors of 40 and 42.

Prime Factorization of 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

Prime Factorization of 42


2 42
3 21
7 7
1

Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 42.

LCM(40,42) = 23×31×51×71
LCM(40,42) = 840

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

Least Common Multiple of 40 and 42 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 42, than apply into the LCM equation.

GCF(40,42) = 2
LCM(40,42) = ( 40 × 42) / 2
LCM(40,42) = 1680 / 2
LCM(40,42) = 840

Properties of LCM 40 and 42

(i) The LCM of 42 and 40 is associative

LCM of 40 and 42 = LCM of 42 and 40

Related Least Common Multiples of 40

Related Least Common Multiples of 42

Frequently Asked Questions on LCM of 40 and 42

1. What is the LCM of 40 and 42?

Answer: LCM of 40 and 42 is 840.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

3. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

4. How to Find the LCM of 40 and 42?

Answer:

Least Common Multiple of 40 and 42 = 840

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

Step 2: Find the prime factorization of 42

42 = 2 x 3 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 = 840 = 2 x 2 x 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 40 and 42 is 840.