Least Common Multiple of 34 and 40

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 40 the smallest integer that is 680 that is divisible by both numbers.

Least Common Multiple (LCM) of 34 and 40 is 680.

LCM(34,40) = 680

LCM of 34 and 40

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

LCM of:
and

Least Common Multiple of 34 and 40

LCM of 34 and 40 is 680

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 40. First we will calculate the prime factors of 34 and 40.

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 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 40.

LCM(34,40) = 23×51×171
LCM(34,40) = 680

Factors of 34

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

1, 2, 17, 34

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

Least Common Multiple of 34 and 40 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 40, than apply into the LCM equation.

GCF(34,40) = 2
LCM(34,40) = ( 34 × 40) / 2
LCM(34,40) = 1360 / 2
LCM(34,40) = 680

Properties of LCM 34 and 40

(i) The LCM of 40 and 34 is associative

LCM of 34 and 40 = LCM of 40 and 34

Related Least Common Multiples of 34

Related Least Common Multiples of 40

Frequently Asked Questions on LCM of 34 and 40

1. What is the LCM of 34 and 40?

Answer: LCM of 34 and 40 is 680.

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 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

4. How to Find the LCM of 34 and 40?

Answer:

Least Common Multiple of 34 and 40 = 680

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

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

LCM = 680 = 2 x 2 x 2 x 5 x 17

Step 4: Therefore, the least common multiple of 34 and 40 is 680.