Least Common Multiple of 38 and 40

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 38 and 40 the smallest integer that is 760 that is divisible by both numbers.

Least Common Multiple (LCM) of 38 and 40 is 760.

LCM(38,40) = 760

LCM of 38 and 40

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

LCM of:
and

Least Common Multiple of 38 and 40

LCM of 38 and 40 is 760

Least common multiple can be found by multiplying the highest exponent prime factors of 38 and 40. First we will calculate the prime factors of 38 and 40.

Prime Factorization of 38


2 38
19 19
1

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 21×191

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

Now multiplying the highest exponent prime factors to calculate the LCM of 38 and 40.

LCM(38,40) = 23×51×191
LCM(38,40) = 760

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

Factors of 40

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

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

Least Common Multiple of 38 and 40 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 40, than apply into the LCM equation.

GCF(38,40) = 2
LCM(38,40) = ( 38 × 40) / 2
LCM(38,40) = 1520 / 2
LCM(38,40) = 760

Properties of LCM 38 and 40

(i) The LCM of 40 and 38 is associative

LCM of 38 and 40 = LCM of 40 and 38

Related Least Common Multiples of 38

Related Least Common Multiples of 40

Frequently Asked Questions on LCM of 38 and 40

1. What is the LCM of 38 and 40?

Answer: LCM of 38 and 40 is 760.

2. What are the Factors of 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

3. 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.

4. How to Find the LCM of 38 and 40?

Answer:

Least Common Multiple of 38 and 40 = 760

Step 1: Find the prime factorization of 38

38 = 2 x 19

Step 2: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

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

LCM = 760 = 2 x 2 x 2 x 5 x 19

Step 4: Therefore, the least common multiple of 38 and 40 is 760.