Least Common Multiple of 1749 and 1755

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1749 and 1755 the smallest integer that is 1023165 that is divisible by both numbers.

Least Common Multiple (LCM) of 1749 and 1755 is 1023165.

LCM(1749,1755) = 1023165

LCM of 1749 and 1755

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

LCM of:
and

Least Common Multiple of 1749 and 1755

LCM of 1749 and 1755 is 1023165

Least common multiple can be found by multiplying the highest exponent prime factors of 1749 and 1755. First we will calculate the prime factors of 1749 and 1755.

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

Prime Factorization of 1755


3 1755
3 585
3 195
5 65
13 13
1

Prime factors of 1755 are 3, 5,13. Prime factorization of 1755 in exponential form is:

1755 = 33×51×131

Now multiplying the highest exponent prime factors to calculate the LCM of 1749 and 1755.

LCM(1749,1755) = 33×51×111×131×531
LCM(1749,1755) = 1023165

Factors of 1749

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

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

Factors of 1755

List of positive integer factors of 1755 that divides 1755 without a remainder.

1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755

Least Common Multiple of 1749 and 1755 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1749 and 1755, than apply into the LCM equation.

GCF(1749,1755) = 3
LCM(1749,1755) = ( 1749 × 1755) / 3
LCM(1749,1755) = 3069495 / 3
LCM(1749,1755) = 1023165

Properties of LCM 1749 and 1755

(i) The LCM of 1755 and 1749 is associative

LCM of 1749 and 1755 = LCM of 1755 and 1749

Related Least Common Multiples of 1749

Related Least Common Multiples of 1755

Frequently Asked Questions on LCM of 1749 and 1755

1. What is the LCM of 1749 and 1755?

Answer: LCM of 1749 and 1755 is 1023165.

2. 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.

3. What are the Factors of 1755?

Answer: Factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755. There are 16 integers that are factors of 1755. The greatest factor of 1755 is 1755.

4. How to Find the LCM of 1749 and 1755?

Answer:

Least Common Multiple of 1749 and 1755 = 1023165

Step 1: Find the prime factorization of 1749

1749 = 3 x 11 x 53

Step 2: Find the prime factorization of 1755

1755 = 3 x 3 x 3 x 5 x 13

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

LCM = 1023165 = 3 x 3 x 3 x 5 x 11 x 13 x 53

Step 4: Therefore, the least common multiple of 1749 and 1755 is 1023165.