Least Common Multiple of 34 and 18

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 34 and 18 the smallest integer that is 306 that is divisible by both numbers.

Least Common Multiple (LCM) of 34 and 18 is 306.

LCM(34,18) = 306

LCM of 34 and 18

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

LCM of:
and

Least Common Multiple of 34 and 18

LCM of 34 and 18 is 306

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 18. First we will calculate the prime factors of 34 and 18.

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

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 18.

LCM(34,18) = 21×32×171
LCM(34,18) = 306

Factors of 34

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

1, 2, 17, 34

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Least Common Multiple of 34 and 18 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 18, than apply into the LCM equation.

GCF(34,18) = 2
LCM(34,18) = ( 34 × 18) / 2
LCM(34,18) = 612 / 2
LCM(34,18) = 306

Properties of LCM 34 and 18

(i) The LCM of 18 and 34 is associative

LCM of 34 and 18 = LCM of 18 and 34

Related Least Common Multiples of 34

Related Least Common Multiples of 18

Frequently Asked Questions on LCM of 34 and 18

1. What is the LCM of 34 and 18?

Answer: LCM of 34 and 18 is 306.

2. 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.

3. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the LCM of 34 and 18?

Answer:

Least Common Multiple of 34 and 18 = 306

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 18

18 = 2 x 3 x 3

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

LCM = 306 = 2 x 3 x 3 x 17

Step 4: Therefore, the least common multiple of 34 and 18 is 306.