Least Common Multiple of 30 and 50

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 50 the smallest integer that is 150 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 50 is 150.

LCM(30,50) = 150

LCM of 30 and 50

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

LCM of:
and

Least Common Multiple of 30 and 50

LCM of 30 and 50 is 150

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 50. First we will calculate the prime factors of 30 and 50.

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 50


2 50
5 25
5 5
1

Prime factors of 50 are 2,5. Prime factorization of 50 in exponential form is:

50 = 21×52

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 50.

LCM(30,50) = 21×31×52
LCM(30,50) = 150

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 50

List of positive integer factors of 50 that divides 50 without a remainder.

1, 2, 5, 10, 25, 50

Least Common Multiple of 30 and 50 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 50, than apply into the LCM equation.

GCF(30,50) = 10
LCM(30,50) = ( 30 × 50) / 10
LCM(30,50) = 1500 / 10
LCM(30,50) = 150

Properties of LCM 30 and 50

(i) The LCM of 50 and 30 is associative

LCM of 30 and 50 = LCM of 50 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 50

Frequently Asked Questions on LCM of 30 and 50

1. What is the LCM of 30 and 50?

Answer: LCM of 30 and 50 is 150.

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 50?

Answer: Factors of 50 are 1, 2, 5, 10, 25, 50. There are 6 integers that are factors of 50. The greatest factor of 50 is 50.

4. How to Find the LCM of 30 and 50?

Answer:

Least Common Multiple of 30 and 50 = 150

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 50

50 = 2 x 5 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 = 150 = 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 30 and 50 is 150.