Least Common Multiple of 30 and 34

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 34 the smallest integer that is 510 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 34 is 510.

LCM(30,34) = 510

LCM of 30 and 34

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

LCM of:
and

Least Common Multiple of 30 and 34

LCM of 30 and 34 is 510

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 34. First we will calculate the prime factors of 30 and 34.

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 34


2 34
17 17
1

Prime factors of 34 are 2,17. Prime factorization of 34 in exponential form is:

34 = 21×171

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 34.

LCM(30,34) = 21×31×51×171
LCM(30,34) = 510

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 34

List of positive integer factors of 34 that divides 34 without a remainder.

1, 2, 17, 34

Least Common Multiple of 30 and 34 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 34, than apply into the LCM equation.

GCF(30,34) = 2
LCM(30,34) = ( 30 × 34) / 2
LCM(30,34) = 1020 / 2
LCM(30,34) = 510

Properties of LCM 30 and 34

(i) The LCM of 34 and 30 is associative

LCM of 30 and 34 = LCM of 34 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 34

Frequently Asked Questions on LCM of 30 and 34

1. What is the LCM of 30 and 34?

Answer: LCM of 30 and 34 is 510.

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 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

4. How to Find the LCM of 30 and 34?

Answer:

Least Common Multiple of 30 and 34 = 510

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 34

34 = 2 x 17

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

LCM = 510 = 2 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 30 and 34 is 510.