Least Common Multiple of 748 and 749

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 748 and 749 the smallest integer that is 560252 that is divisible by both numbers.

Least Common Multiple (LCM) of 748 and 749 is 560252.

LCM(748,749) = 560252

LCM of 748 and 749

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

LCM of:
and

Least Common Multiple of 748 and 749

LCM of 748 and 749 is 560252

Least common multiple can be found by multiplying the highest exponent prime factors of 748 and 749. First we will calculate the prime factors of 748 and 749.

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

Prime Factorization of 749


7 749
107 107
1

Prime factors of 749 are 7,107. Prime factorization of 749 in exponential form is:

749 = 71×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 748 and 749.

LCM(748,749) = 22×71×111×171×1071
LCM(748,749) = 560252

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

Factors of 749

List of positive integer factors of 749 that divides 749 without a remainder.

1, 7, 107, 749

Least Common Multiple of 748 and 749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 748 and 749, than apply into the LCM equation.

GCF(748,749) = 1
LCM(748,749) = ( 748 × 749) / 1
LCM(748,749) = 560252 / 1
LCM(748,749) = 560252

Properties of LCM 748 and 749

(i) The LCM of 749 and 748 is associative

LCM of 748 and 749 = LCM of 749 and 748

Related Least Common Multiples of 748

Related Least Common Multiples of 749

Frequently Asked Questions on LCM of 748 and 749

1. What is the LCM of 748 and 749?

Answer: LCM of 748 and 749 is 560252.

2. 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.

3. What are the Factors of 749?

Answer: Factors of 749 are 1, 7, 107, 749. There are 4 integers that are factors of 749. The greatest factor of 749 is 749.

4. How to Find the LCM of 748 and 749?

Answer:

Least Common Multiple of 748 and 749 = 560252

Step 1: Find the prime factorization of 748

748 = 2 x 2 x 11 x 17

Step 2: Find the prime factorization of 749

749 = 7 x 107

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

LCM = 560252 = 2 x 2 x 7 x 11 x 17 x 107

Step 4: Therefore, the least common multiple of 748 and 749 is 560252.