Least Common Multiple of 1746 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 1746 and 1749 the smallest integer that is 1017918 that is divisible by both numbers.

Least Common Multiple (LCM) of 1746 and 1749 is 1017918.

LCM(1746,1749) = 1017918

LCM of 1746 and 1749

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

LCM of:
and

Least Common Multiple of 1746 and 1749

LCM of 1746 and 1749 is 1017918

Least common multiple can be found by multiplying the highest exponent prime factors of 1746 and 1749. First we will calculate the prime factors of 1746 and 1749.

Prime Factorization of 1746


2 1746
3 873
3 291
97 97
1

Prime factors of 1746 are 2, 3,97. Prime factorization of 1746 in exponential form is:

1746 = 21×32×971

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 1746 and 1749.

LCM(1746,1749) = 21×32×111×531×971
LCM(1746,1749) = 1017918

Factors of 1746

List of positive integer factors of 1746 that divides 1746 without a remainder.

1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746

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 1746 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 1746 and 1749, than apply into the LCM equation.

GCF(1746,1749) = 3
LCM(1746,1749) = ( 1746 × 1749) / 3
LCM(1746,1749) = 3053754 / 3
LCM(1746,1749) = 1017918

Properties of LCM 1746 and 1749

(i) The LCM of 1749 and 1746 is associative

LCM of 1746 and 1749 = LCM of 1749 and 1746

Related Least Common Multiples of 1746

Related Least Common Multiples of 1749

Frequently Asked Questions on LCM of 1746 and 1749

1. What is the LCM of 1746 and 1749?

Answer: LCM of 1746 and 1749 is 1017918.

2. What are the Factors of 1746?

Answer: Factors of 1746 are 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746. There are 12 integers that are factors of 1746. The greatest factor of 1746 is 1746.

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 1746 and 1749?

Answer:

Least Common Multiple of 1746 and 1749 = 1017918

Step 1: Find the prime factorization of 1746

1746 = 2 x 3 x 3 x 97

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 = 1017918 = 2 x 3 x 3 x 11 x 53 x 97

Step 4: Therefore, the least common multiple of 1746 and 1749 is 1017918.