Least Common Multiple of 742 and 748

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 742 and 748 the smallest integer that is 277508 that is divisible by both numbers.

Least Common Multiple (LCM) of 742 and 748 is 277508.

LCM(742,748) = 277508

LCM of 742 and 748

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

LCM of:
and

Least Common Multiple of 742 and 748

LCM of 742 and 748 is 277508

Least common multiple can be found by multiplying the highest exponent prime factors of 742 and 748. First we will calculate the prime factors of 742 and 748.

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

Prime Factorization of 748


2 748
2 374
11 187
17 17
1

Prime factors of 748 are 2, 11,17. Prime factorization of 748 in exponential form is:

748 = 22×111×171

Now multiplying the highest exponent prime factors to calculate the LCM of 742 and 748.

LCM(742,748) = 22×71×111×171×531
LCM(742,748) = 277508

Factors of 742

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

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

Factors of 748

List of positive integer factors of 748 that divides 748 without a remainder.

1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748

Least Common Multiple of 742 and 748 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 742 and 748, than apply into the LCM equation.

GCF(742,748) = 2
LCM(742,748) = ( 742 × 748) / 2
LCM(742,748) = 555016 / 2
LCM(742,748) = 277508

Properties of LCM 742 and 748

(i) The LCM of 748 and 742 is associative

LCM of 742 and 748 = LCM of 748 and 742

Related Least Common Multiples of 742

Related Least Common Multiples of 748

Frequently Asked Questions on LCM of 742 and 748

1. What is the LCM of 742 and 748?

Answer: LCM of 742 and 748 is 277508.

2. 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.

3. What are the Factors of 748?

Answer: Factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748. There are 12 integers that are factors of 748. The greatest factor of 748 is 748.

4. How to Find the LCM of 742 and 748?

Answer:

Least Common Multiple of 742 and 748 = 277508

Step 1: Find the prime factorization of 742

742 = 2 x 7 x 53

Step 2: Find the prime factorization of 748

748 = 2 x 2 x 11 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 = 277508 = 2 x 2 x 7 x 11 x 17 x 53

Step 4: Therefore, the least common multiple of 742 and 748 is 277508.