Least Common Multiple of 30 and 38

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 38 the smallest integer that is 570 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 38 is 570.

LCM(30,38) = 570

LCM of 30 and 38

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

LCM of:
and

Least Common Multiple of 30 and 38

LCM of 30 and 38 is 570

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 38. First we will calculate the prime factors of 30 and 38.

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 38


2 38
19 19
1

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

38 = 21×191

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 38.

LCM(30,38) = 21×31×51×191
LCM(30,38) = 570

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 38

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

1, 2, 19, 38

Least Common Multiple of 30 and 38 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 38, than apply into the LCM equation.

GCF(30,38) = 2
LCM(30,38) = ( 30 × 38) / 2
LCM(30,38) = 1140 / 2
LCM(30,38) = 570

Properties of LCM 30 and 38

(i) The LCM of 38 and 30 is associative

LCM of 30 and 38 = LCM of 38 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 38

Frequently Asked Questions on LCM of 30 and 38

1. What is the LCM of 30 and 38?

Answer: LCM of 30 and 38 is 570.

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 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.

4. How to Find the LCM of 30 and 38?

Answer:

Least Common Multiple of 30 and 38 = 570

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 38

38 = 2 x 19

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

LCM = 570 = 2 x 3 x 5 x 19

Step 4: Therefore, the least common multiple of 30 and 38 is 570.