Least Common Multiple of 1744 and 1748

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1744 and 1748 the smallest integer that is 762128 that is divisible by both numbers.

Least Common Multiple (LCM) of 1744 and 1748 is 762128.

LCM(1744,1748) = 762128

LCM of 1744 and 1748

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

LCM of:
and

Least Common Multiple of 1744 and 1748

LCM of 1744 and 1748 is 762128

Least common multiple can be found by multiplying the highest exponent prime factors of 1744 and 1748. First we will calculate the prime factors of 1744 and 1748.

Prime Factorization of 1744


2 1744
2 872
2 436
2 218
109 109
1

Prime factors of 1744 are 2,109. Prime factorization of 1744 in exponential form is:

1744 = 24×1091

Prime Factorization of 1748


2 1748
2 874
19 437
23 23
1

Prime factors of 1748 are 2, 19,23. Prime factorization of 1748 in exponential form is:

1748 = 22×191×231

Now multiplying the highest exponent prime factors to calculate the LCM of 1744 and 1748.

LCM(1744,1748) = 24×191×231×1091
LCM(1744,1748) = 762128

Factors of 1744

List of positive integer factors of 1744 that divides 1744 without a remainder.

1, 2, 4, 8, 16, 109, 218, 436, 872, 1744

Factors of 1748

List of positive integer factors of 1748 that divides 1748 without a remainder.

1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748

Least Common Multiple of 1744 and 1748 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1744 and 1748, than apply into the LCM equation.

GCF(1744,1748) = 4
LCM(1744,1748) = ( 1744 × 1748) / 4
LCM(1744,1748) = 3048512 / 4
LCM(1744,1748) = 762128

Properties of LCM 1744 and 1748

(i) The LCM of 1748 and 1744 is associative

LCM of 1744 and 1748 = LCM of 1748 and 1744

Related Least Common Multiples of 1744

Related Least Common Multiples of 1748

Frequently Asked Questions on LCM of 1744 and 1748

1. What is the LCM of 1744 and 1748?

Answer: LCM of 1744 and 1748 is 762128.

2. What are the Factors of 1744?

Answer: Factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744. There are 10 integers that are factors of 1744. The greatest factor of 1744 is 1744.

3. What are the Factors of 1748?

Answer: Factors of 1748 are 1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748. There are 12 integers that are factors of 1748. The greatest factor of 1748 is 1748.

4. How to Find the LCM of 1744 and 1748?

Answer:

Least Common Multiple of 1744 and 1748 = 762128

Step 1: Find the prime factorization of 1744

1744 = 2 x 2 x 2 x 2 x 109

Step 2: Find the prime factorization of 1748

1748 = 2 x 2 x 19 x 23

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

LCM = 762128 = 2 x 2 x 2 x 2 x 19 x 23 x 109

Step 4: Therefore, the least common multiple of 1744 and 1748 is 762128.