Least Common Multiple of 34 and 38

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 38 the smallest integer that is 646 that is divisible by both numbers.

Least Common Multiple (LCM) of 34 and 38 is 646.

LCM(34,38) = 646

LCM of 34 and 38

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

LCM of:
and

Least Common Multiple of 34 and 38

LCM of 34 and 38 is 646

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 38. First we will calculate the prime factors of 34 and 38.

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 38


2 38
19 19
1

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 21×191

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 38.

LCM(34,38) = 21×171×191
LCM(34,38) = 646

Factors of 34

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

1, 2, 17, 34

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

Least Common Multiple of 34 and 38 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 38, than apply into the LCM equation.

GCF(34,38) = 2
LCM(34,38) = ( 34 × 38) / 2
LCM(34,38) = 1292 / 2
LCM(34,38) = 646

Properties of LCM 34 and 38

(i) The LCM of 38 and 34 is associative

LCM of 34 and 38 = LCM of 38 and 34

Related Least Common Multiples of 34

Related Least Common Multiples of 38

Frequently Asked Questions on LCM of 34 and 38

1. What is the LCM of 34 and 38?

Answer: LCM of 34 and 38 is 646.

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 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the LCM of 34 and 38?

Answer:

Least Common Multiple of 34 and 38 = 646

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 38

38 = 2 x 19

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

LCM = 646 = 2 x 17 x 19

Step 4: Therefore, the least common multiple of 34 and 38 is 646.