Least Common Multiple of 7740 and 7742

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7740 and 7742 the smallest integer that is 29961540 that is divisible by both numbers.

Least Common Multiple (LCM) of 7740 and 7742 is 29961540.

LCM(7740,7742) = 29961540

LCM of 7740 and 7742

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

LCM of:
and

Least Common Multiple of 7740 and 7742

LCM of 7740 and 7742 is 29961540

Least common multiple can be found by multiplying the highest exponent prime factors of 7740 and 7742. First we will calculate the prime factors of 7740 and 7742.

Prime Factorization of 7740


2 7740
2 3870
3 1935
3 645
5 215
43 43
1

Prime factors of 7740 are 2, 3, 5,43. Prime factorization of 7740 in exponential form is:

7740 = 22×32×51×431

Prime Factorization of 7742


2 7742
7 3871
7 553
79 79
1

Prime factors of 7742 are 2, 7,79. Prime factorization of 7742 in exponential form is:

7742 = 21×72×791

Now multiplying the highest exponent prime factors to calculate the LCM of 7740 and 7742.

LCM(7740,7742) = 22×32×51×72×431×791
LCM(7740,7742) = 29961540

Factors of 7740

List of positive integer factors of 7740 that divides 7740 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870, 7740

Factors of 7742

List of positive integer factors of 7742 that divides 7742 without a remainder.

1, 2, 7, 14, 49, 79, 98, 158, 553, 1106, 3871, 7742

Least Common Multiple of 7740 and 7742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7740 and 7742, than apply into the LCM equation.

GCF(7740,7742) = 2
LCM(7740,7742) = ( 7740 × 7742) / 2
LCM(7740,7742) = 59923080 / 2
LCM(7740,7742) = 29961540

Properties of LCM 7740 and 7742

(i) The LCM of 7742 and 7740 is associative

LCM of 7740 and 7742 = LCM of 7742 and 7740

Related Least Common Multiples of 7740

Related Least Common Multiples of 7742

Frequently Asked Questions on LCM of 7740 and 7742

1. What is the LCM of 7740 and 7742?

Answer: LCM of 7740 and 7742 is 29961540.

2. What are the Factors of 7740?

Answer: Factors of 7740 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870, 7740. There are 36 integers that are factors of 7740. The greatest factor of 7740 is 7740.

3. What are the Factors of 7742?

Answer: Factors of 7742 are 1, 2, 7, 14, 49, 79, 98, 158, 553, 1106, 3871, 7742. There are 12 integers that are factors of 7742. The greatest factor of 7742 is 7742.

4. How to Find the LCM of 7740 and 7742?

Answer:

Least Common Multiple of 7740 and 7742 = 29961540

Step 1: Find the prime factorization of 7740

7740 = 2 x 2 x 3 x 3 x 5 x 43

Step 2: Find the prime factorization of 7742

7742 = 2 x 7 x 7 x 79

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

LCM = 29961540 = 2 x 2 x 3 x 3 x 5 x 7 x 7 x 43 x 79

Step 4: Therefore, the least common multiple of 7740 and 7742 is 29961540.