Least Common Multiple of 1744 and 1749

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 1749 the smallest integer that is 3050256 that is divisible by both numbers.

Least Common Multiple (LCM) of 1744 and 1749 is 3050256.

LCM(1744,1749) = 3050256

LCM of 1744 and 1749

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

LCM of:
and

Least Common Multiple of 1744 and 1749

LCM of 1744 and 1749 is 3050256

Least common multiple can be found by multiplying the highest exponent prime factors of 1744 and 1749. First we will calculate the prime factors of 1744 and 1749.

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 1749


3 1749
11 583
53 53
1

Prime factors of 1749 are 3, 11,53. Prime factorization of 1749 in exponential form is:

1749 = 31×111×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1744 and 1749.

LCM(1744,1749) = 24×31×111×531×1091
LCM(1744,1749) = 3050256

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 1749

List of positive integer factors of 1749 that divides 1749 without a remainder.

1, 3, 11, 33, 53, 159, 583, 1749

Least Common Multiple of 1744 and 1749 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 1749, than apply into the LCM equation.

GCF(1744,1749) = 1
LCM(1744,1749) = ( 1744 × 1749) / 1
LCM(1744,1749) = 3050256 / 1
LCM(1744,1749) = 3050256

Properties of LCM 1744 and 1749

(i) The LCM of 1749 and 1744 is associative

LCM of 1744 and 1749 = LCM of 1749 and 1744

Related Least Common Multiples of 1744

Related Least Common Multiples of 1749

Frequently Asked Questions on LCM of 1744 and 1749

1. What is the LCM of 1744 and 1749?

Answer: LCM of 1744 and 1749 is 3050256.

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 1749?

Answer: Factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749. There are 8 integers that are factors of 1749. The greatest factor of 1749 is 1749.

4. How to Find the LCM of 1744 and 1749?

Answer:

Least Common Multiple of 1744 and 1749 = 3050256

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 1749

1749 = 3 x 11 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 = 3050256 = 2 x 2 x 2 x 2 x 3 x 11 x 53 x 109

Step 4: Therefore, the least common multiple of 1744 and 1749 is 3050256.