Least Common Multiple of 1744 and 1752

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 1752 the smallest integer that is 381936 that is divisible by both numbers.

Least Common Multiple (LCM) of 1744 and 1752 is 381936.

LCM(1744,1752) = 381936

LCM of 1744 and 1752

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

LCM of:
and

Least Common Multiple of 1744 and 1752

LCM of 1744 and 1752 is 381936

Least common multiple can be found by multiplying the highest exponent prime factors of 1744 and 1752. First we will calculate the prime factors of 1744 and 1752.

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 1752


2 1752
2 876
2 438
3 219
73 73
1

Prime factors of 1752 are 2, 3,73. Prime factorization of 1752 in exponential form is:

1752 = 23×31×731

Now multiplying the highest exponent prime factors to calculate the LCM of 1744 and 1752.

LCM(1744,1752) = 24×31×731×1091
LCM(1744,1752) = 381936

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 1752

List of positive integer factors of 1752 that divides 1752 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752

Least Common Multiple of 1744 and 1752 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 1752, than apply into the LCM equation.

GCF(1744,1752) = 8
LCM(1744,1752) = ( 1744 × 1752) / 8
LCM(1744,1752) = 3055488 / 8
LCM(1744,1752) = 381936

Properties of LCM 1744 and 1752

(i) The LCM of 1752 and 1744 is associative

LCM of 1744 and 1752 = LCM of 1752 and 1744

Related Least Common Multiples of 1744

Related Least Common Multiples of 1752

Frequently Asked Questions on LCM of 1744 and 1752

1. What is the LCM of 1744 and 1752?

Answer: LCM of 1744 and 1752 is 381936.

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 1752?

Answer: Factors of 1752 are 1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752. There are 16 integers that are factors of 1752. The greatest factor of 1752 is 1752.

4. How to Find the LCM of 1744 and 1752?

Answer:

Least Common Multiple of 1744 and 1752 = 381936

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 1752

1752 = 2 x 2 x 2 x 3 x 73

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

LCM = 381936 = 2 x 2 x 2 x 2 x 3 x 73 x 109

Step 4: Therefore, the least common multiple of 1744 and 1752 is 381936.