Least Common Multiple of 7734 and 7740

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7734 and 7740 the smallest integer that is 9976860 that is divisible by both numbers.

Least Common Multiple (LCM) of 7734 and 7740 is 9976860.

LCM(7734,7740) = 9976860

LCM of 7734 and 7740

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

LCM of:
and

Least Common Multiple of 7734 and 7740

LCM of 7734 and 7740 is 9976860

Least common multiple can be found by multiplying the highest exponent prime factors of 7734 and 7740. First we will calculate the prime factors of 7734 and 7740.

Prime Factorization of 7734


2 7734
3 3867
1289 1289
1

Prime factors of 7734 are 2, 3,1289. Prime factorization of 7734 in exponential form is:

7734 = 21×31×12891

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

Now multiplying the highest exponent prime factors to calculate the LCM of 7734 and 7740.

LCM(7734,7740) = 22×32×51×431×12891
LCM(7734,7740) = 9976860

Factors of 7734

List of positive integer factors of 7734 that divides 7734 without a remainder.

1, 2, 3, 6, 1289, 2578, 3867, 7734

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

Least Common Multiple of 7734 and 7740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7734 and 7740, than apply into the LCM equation.

GCF(7734,7740) = 6
LCM(7734,7740) = ( 7734 × 7740) / 6
LCM(7734,7740) = 59861160 / 6
LCM(7734,7740) = 9976860

Properties of LCM 7734 and 7740

(i) The LCM of 7740 and 7734 is associative

LCM of 7734 and 7740 = LCM of 7740 and 7734

Related Least Common Multiples of 7734

Related Least Common Multiples of 7740

Frequently Asked Questions on LCM of 7734 and 7740

1. What is the LCM of 7734 and 7740?

Answer: LCM of 7734 and 7740 is 9976860.

2. What are the Factors of 7734?

Answer: Factors of 7734 are 1, 2, 3, 6, 1289, 2578, 3867, 7734. There are 8 integers that are factors of 7734. The greatest factor of 7734 is 7734.

3. 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.

4. How to Find the LCM of 7734 and 7740?

Answer:

Least Common Multiple of 7734 and 7740 = 9976860

Step 1: Find the prime factorization of 7734

7734 = 2 x 3 x 1289

Step 2: Find the prime factorization of 7740

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

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

LCM = 9976860 = 2 x 2 x 3 x 3 x 5 x 43 x 1289

Step 4: Therefore, the least common multiple of 7734 and 7740 is 9976860.