Least Common Multiple of 35 and 51

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 35 and 51 the smallest integer that is 1785 that is divisible by both numbers.

Least Common Multiple (LCM) of 35 and 51 is 1785.

LCM(35,51) = 1785

LCM of 35 and 51

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

LCM of:
and

Least Common Multiple of 35 and 51

LCM of 35 and 51 is 1785

Least common multiple can be found by multiplying the highest exponent prime factors of 35 and 51. First we will calculate the prime factors of 35 and 51.

Prime Factorization of 35


5 35
7 7
1

Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:

35 = 51×71

Prime Factorization of 51


3 51
17 17
1

Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:

51 = 31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 35 and 51.

LCM(35,51) = 31×51×71×171
LCM(35,51) = 1785

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1, 5, 7, 35

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1, 3, 17, 51

Least Common Multiple of 35 and 51 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35 and 51, than apply into the LCM equation.

GCF(35,51) = 1
LCM(35,51) = ( 35 × 51) / 1
LCM(35,51) = 1785 / 1
LCM(35,51) = 1785

Properties of LCM 35 and 51

(i) The LCM of 51 and 35 is associative

LCM of 35 and 51 = LCM of 51 and 35

Related Least Common Multiples of 35

Related Least Common Multiples of 51

Frequently Asked Questions on LCM of 35 and 51

1. What is the LCM of 35 and 51?

Answer: LCM of 35 and 51 is 1785.

2. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

3. What are the Factors of 51?

Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.

4. How to Find the LCM of 35 and 51?

Answer:

Least Common Multiple of 35 and 51 = 1785

Step 1: Find the prime factorization of 35

35 = 5 x 7

Step 2: Find the prime factorization of 51

51 = 3 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 = 1785 = 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 35 and 51 is 1785.