Least Common Multiple of 30 and 70

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 70 the smallest integer that is 210 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 70 is 210.

LCM(30,70) = 210

LCM of 30 and 70

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

LCM of:
and

Least Common Multiple of 30 and 70

LCM of 30 and 70 is 210

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 70. First we will calculate the prime factors of 30 and 70.

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 70


2 70
5 35
7 7
1

Prime factors of 70 are 2, 5,7. Prime factorization of 70 in exponential form is:

70 = 21×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 70.

LCM(30,70) = 21×31×51×71
LCM(30,70) = 210

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 70

List of positive integer factors of 70 that divides 70 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70

Least Common Multiple of 30 and 70 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 70, than apply into the LCM equation.

GCF(30,70) = 10
LCM(30,70) = ( 30 × 70) / 10
LCM(30,70) = 2100 / 10
LCM(30,70) = 210

Properties of LCM 30 and 70

(i) The LCM of 70 and 30 is associative

LCM of 30 and 70 = LCM of 70 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 70

Frequently Asked Questions on LCM of 30 and 70

1. What is the LCM of 30 and 70?

Answer: LCM of 30 and 70 is 210.

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 70?

Answer: Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70. There are 8 integers that are factors of 70. The greatest factor of 70 is 70.

4. How to Find the LCM of 30 and 70?

Answer:

Least Common Multiple of 30 and 70 = 210

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 70

70 = 2 x 5 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 = 210 = 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 30 and 70 is 210.