Least Common Multiple of 1740 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 1740 and 1748 the smallest integer that is 760380 that is divisible by both numbers.

Least Common Multiple (LCM) of 1740 and 1748 is 760380.

LCM(1740,1748) = 760380

LCM of 1740 and 1748

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

LCM of:
and

Least Common Multiple of 1740 and 1748

LCM of 1740 and 1748 is 760380

Least common multiple can be found by multiplying the highest exponent prime factors of 1740 and 1748. First we will calculate the prime factors of 1740 and 1748.

Prime Factorization of 1740


2 1740
2 870
3 435
5 145
29 29
1

Prime factors of 1740 are 2, 3, 5,29. Prime factorization of 1740 in exponential form is:

1740 = 22×31×51×291

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 1740 and 1748.

LCM(1740,1748) = 22×31×51×191×231×291
LCM(1740,1748) = 760380

Factors of 1740

List of positive integer factors of 1740 that divides 1740 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, 1740

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 1740 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 1740 and 1748, than apply into the LCM equation.

GCF(1740,1748) = 4
LCM(1740,1748) = ( 1740 × 1748) / 4
LCM(1740,1748) = 3041520 / 4
LCM(1740,1748) = 760380

Properties of LCM 1740 and 1748

(i) The LCM of 1748 and 1740 is associative

LCM of 1740 and 1748 = LCM of 1748 and 1740

Related Least Common Multiples of 1740

Related Least Common Multiples of 1748

Frequently Asked Questions on LCM of 1740 and 1748

1. What is the LCM of 1740 and 1748?

Answer: LCM of 1740 and 1748 is 760380.

2. What are the Factors of 1740?

Answer: Factors of 1740 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, 1740. There are 24 integers that are factors of 1740. The greatest factor of 1740 is 1740.

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 1740 and 1748?

Answer:

Least Common Multiple of 1740 and 1748 = 760380

Step 1: Find the prime factorization of 1740

1740 = 2 x 2 x 3 x 5 x 29

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 = 760380 = 2 x 2 x 3 x 5 x 19 x 23 x 29

Step 4: Therefore, the least common multiple of 1740 and 1748 is 760380.