Least Common Multiple of 1740 and 1746

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 1746 the smallest integer that is 506340 that is divisible by both numbers.

Least Common Multiple (LCM) of 1740 and 1746 is 506340.

LCM(1740,1746) = 506340

LCM of 1740 and 1746

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

LCM of:
and

Least Common Multiple of 1740 and 1746

LCM of 1740 and 1746 is 506340

Least common multiple can be found by multiplying the highest exponent prime factors of 1740 and 1746. First we will calculate the prime factors of 1740 and 1746.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 1740 and 1746.

LCM(1740,1746) = 22×32×51×291×971
LCM(1740,1746) = 506340

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 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

Least Common Multiple of 1740 and 1746 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 1746, than apply into the LCM equation.

GCF(1740,1746) = 6
LCM(1740,1746) = ( 1740 × 1746) / 6
LCM(1740,1746) = 3038040 / 6
LCM(1740,1746) = 506340

Properties of LCM 1740 and 1746

(i) The LCM of 1746 and 1740 is associative

LCM of 1740 and 1746 = LCM of 1746 and 1740

Related Least Common Multiples of 1740

Related Least Common Multiples of 1746

Frequently Asked Questions on LCM of 1740 and 1746

1. What is the LCM of 1740 and 1746?

Answer: LCM of 1740 and 1746 is 506340.

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 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.

4. How to Find the LCM of 1740 and 1746?

Answer:

Least Common Multiple of 1740 and 1746 = 506340

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 1746

1746 = 2 x 3 x 3 x 97

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

LCM = 506340 = 2 x 2 x 3 x 3 x 5 x 29 x 97

Step 4: Therefore, the least common multiple of 1740 and 1746 is 506340.