Least Common Multiple of 30 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 30 and 40 the smallest integer that is 120 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 40 is 120.

LCM(30,40) = 120

LCM of 30 and 40

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

LCM of:
and

Least Common Multiple of 30 and 40

LCM of 30 and 40 is 120

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 40. First we will calculate the prime factors of 30 and 40.

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

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 30 and 40.

LCM(30,40) = 23×31×51
LCM(30,40) = 120

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

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 30 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 30 and 40, than apply into the LCM equation.

GCF(30,40) = 10
LCM(30,40) = ( 30 × 40) / 10
LCM(30,40) = 1200 / 10
LCM(30,40) = 120

Properties of LCM 30 and 40

(i) The LCM of 40 and 30 is associative

LCM of 30 and 40 = LCM of 40 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 40

Frequently Asked Questions on LCM of 30 and 40

1. What is the LCM of 30 and 40?

Answer: LCM of 30 and 40 is 120.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

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 30 and 40?

Answer:

Least Common Multiple of 30 and 40 = 120

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 = 120 = 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 30 and 40 is 120.