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Least Common Multiple of 735 and 742

Free LCM Calculator determines the least common multiple (LCM) between 735 and 742 the smallest integer that is 77910 that is divisible by both numbers.

Least Common Multiple (LCM) of 735 and 742 is 77910.

LCM(735,742) = 77910

LCM of 735 and 742

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

LCM of:
and

Least Common Multiple (LCM) of 735 and 742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 735 and 742. First we will calculate the prime factors of 735 and 742.

Prime Factorization of 735


3 735
5 245
7 49
7 7
1

Prime factors of 735 are 3, 5,7. Prime factorization of 735 in exponential form is:

735 = 31×51×72

Prime Factorization of 742


2 742
7 371
53 53
1

Prime factors of 742 are 2, 7,53. Prime factorization of 742 in exponential form is:

742 = 21×71×531

Now multiplying the highest exponent prime factors to calculate the LCM of 735 and 742.

LCM(735,742) = 21×31×51×72×531
LCM(735,742) = 77910

Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735

Factors of 742

List of positive integer factors of 742 that divides 742 without a remainder.

1, 2, 7, 14, 53, 106, 371, 742

Least Common Multiple of 735 and 742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 735 and 742, than apply into the LCM equation.

GCF(735,742) = 7
LCM(735,742) = ( 735 × 742) / 7
LCM(735,742) = 545370 / 7
LCM(735,742) = 77910

Properties of LCM 735 and 742

(i) The LCM of 742 and 735 is associative

LCM of 735 and 742 = LCM of 742 and 735

Frequently Asked Questions on LCM of 735 and 742

1. What is the LCM of 735 and 742?

Answer: LCM of 735 and 742 is 77910.

2. What are the Factors of 735?

Answer: Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. There are 12 integers that are factors of 735. The greatest factor of 735 is 735.

3. What are the Factors of 742?

Answer: Factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742. There are 8 integers that are factors of 742. The greatest factor of 742 is 742.

4. How to Find the LCM of 735 and 742?

Answer:

Least Common Multiple of 735 and 742 = 77910

Step 1: Find the prime factorization of 735

735 = 3 x 5 x 7 x 7

Step 2: Find the prime factorization of 742

742 = 2 x 7 x 53

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

LCM = 77910 = 2 x 3 x 5 x 7 x 7 x 53

Step 4: Therefore, the least common multiple of 735 and 742 is 77910.