Least Common Multiple of 65 and 70

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 65 and 70 the smallest integer that is 910 that is divisible by both numbers.

Least Common Multiple (LCM) of 65 and 70 is 910.

LCM(65,70) = 910

LCM of 65 and 70

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

LCM of:
and

Least Common Multiple of 65 and 70

LCM of 65 and 70 is 910

Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 70. First we will calculate the prime factors of 65 and 70.

Prime Factorization of 65


5 65
13 13
1

Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:

65 = 51×131

Prime Factorization of 70


2 70
5 35
7 7
1

Prime factors of 70 are 2, 5,7. Prime factorization of 70 in exponential form is:

70 = 21×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 70.

LCM(65,70) = 21×51×71×131
LCM(65,70) = 910

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1, 5, 13, 65

Factors of 70

List of positive integer factors of 70 that divides 70 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70

Least Common Multiple of 65 and 70 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 70, than apply into the LCM equation.

GCF(65,70) = 5
LCM(65,70) = ( 65 × 70) / 5
LCM(65,70) = 4550 / 5
LCM(65,70) = 910

Properties of LCM 65 and 70

(i) The LCM of 70 and 65 is associative

LCM of 65 and 70 = LCM of 70 and 65

Related Least Common Multiples of 65

Related Least Common Multiples of 70

Frequently Asked Questions on LCM of 65 and 70

1. What is the LCM of 65 and 70?

Answer: LCM of 65 and 70 is 910.

2. What are the Factors of 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

3. What are the Factors of 70?

Answer: Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70. There are 8 integers that are factors of 70. The greatest factor of 70 is 70.

4. How to Find the LCM of 65 and 70?

Answer:

Least Common Multiple of 65 and 70 = 910

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 70

70 = 2 x 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 = 910 = 2 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 65 and 70 is 910.