Least Common Multiple of 30 and 35

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

Least Common Multiple (LCM) of 30 and 35 is 210.

LCM(30,35) = 210

LCM of 30 and 35

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

LCM of:
and

Least Common Multiple of 30 and 35

LCM of 30 and 35 is 210

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 35. First we will calculate the prime factors of 30 and 35.

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 35


5 35
7 7
1

Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:

35 = 51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 35.

LCM(30,35) = 21×31×51×71
LCM(30,35) = 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 35

List of positive integer factors of 35 that divides 35 without a remainder.

1, 5, 7, 35

Least Common Multiple of 30 and 35 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 35, than apply into the LCM equation.

GCF(30,35) = 5
LCM(30,35) = ( 30 × 35) / 5
LCM(30,35) = 1050 / 5
LCM(30,35) = 210

Properties of LCM 30 and 35

(i) The LCM of 35 and 30 is associative

LCM of 30 and 35 = LCM of 35 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 35

Frequently Asked Questions on LCM of 30 and 35

1. What is the LCM of 30 and 35?

Answer: LCM of 30 and 35 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 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. How to Find the LCM of 30 and 35?

Answer:

Least Common Multiple of 30 and 35 = 210

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 35

35 = 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 35 is 210.