Least Common Multiple of 7734 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 7734 and 7742 the smallest integer that is 29938314 that is divisible by both numbers.

Least Common Multiple (LCM) of 7734 and 7742 is 29938314.

LCM(7734,7742) = 29938314

LCM of 7734 and 7742

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

LCM of:
and

Least Common Multiple of 7734 and 7742

LCM of 7734 and 7742 is 29938314

Least common multiple can be found by multiplying the highest exponent prime factors of 7734 and 7742. First we will calculate the prime factors of 7734 and 7742.

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 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 7734 and 7742.

LCM(7734,7742) = 21×31×72×791×12891
LCM(7734,7742) = 29938314

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 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 7734 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 7734 and 7742, than apply into the LCM equation.

GCF(7734,7742) = 2
LCM(7734,7742) = ( 7734 × 7742) / 2
LCM(7734,7742) = 59876628 / 2
LCM(7734,7742) = 29938314

Properties of LCM 7734 and 7742

(i) The LCM of 7742 and 7734 is associative

LCM of 7734 and 7742 = LCM of 7742 and 7734

Related Least Common Multiples of 7734

Related Least Common Multiples of 7742

Frequently Asked Questions on LCM of 7734 and 7742

1. What is the LCM of 7734 and 7742?

Answer: LCM of 7734 and 7742 is 29938314.

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 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 7734 and 7742?

Answer:

Least Common Multiple of 7734 and 7742 = 29938314

Step 1: Find the prime factorization of 7734

7734 = 2 x 3 x 1289

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 = 29938314 = 2 x 3 x 7 x 7 x 79 x 1289

Step 4: Therefore, the least common multiple of 7734 and 7742 is 29938314.