Least Common Multiple of 7704 and 7712

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7704 and 7712 the smallest integer that is 7426656 that is divisible by both numbers.

Least Common Multiple (LCM) of 7704 and 7712 is 7426656.

LCM(7704,7712) = 7426656

LCM of 7704 and 7712

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

LCM of:
and

Least Common Multiple of 7704 and 7712

LCM of 7704 and 7712 is 7426656

Least common multiple can be found by multiplying the highest exponent prime factors of 7704 and 7712. First we will calculate the prime factors of 7704 and 7712.

Prime Factorization of 7704


2 7704
2 3852
2 1926
3 963
3 321
107 107
1

Prime factors of 7704 are 2, 3,107. Prime factorization of 7704 in exponential form is:

7704 = 23×32×1071

Prime Factorization of 7712


2 7712
2 3856
2 1928
2 964
2 482
241 241
1

Prime factors of 7712 are 2,241. Prime factorization of 7712 in exponential form is:

7712 = 25×2411

Now multiplying the highest exponent prime factors to calculate the LCM of 7704 and 7712.

LCM(7704,7712) = 25×32×1071×2411
LCM(7704,7712) = 7426656

Factors of 7704

List of positive integer factors of 7704 that divides 7704 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 107, 214, 321, 428, 642, 856, 963, 1284, 1926, 2568, 3852, 7704

Factors of 7712

List of positive integer factors of 7712 that divides 7712 without a remainder.

1, 2, 4, 8, 16, 32, 241, 482, 964, 1928, 3856, 7712

Least Common Multiple of 7704 and 7712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7704 and 7712, than apply into the LCM equation.

GCF(7704,7712) = 8
LCM(7704,7712) = ( 7704 × 7712) / 8
LCM(7704,7712) = 59413248 / 8
LCM(7704,7712) = 7426656

Properties of LCM 7704 and 7712

(i) The LCM of 7712 and 7704 is associative

LCM of 7704 and 7712 = LCM of 7712 and 7704

Related Least Common Multiples of 7704

Related Least Common Multiples of 7712

Frequently Asked Questions on LCM of 7704 and 7712

1. What is the LCM of 7704 and 7712?

Answer: LCM of 7704 and 7712 is 7426656.

2. What are the Factors of 7704?

Answer: Factors of 7704 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 107, 214, 321, 428, 642, 856, 963, 1284, 1926, 2568, 3852, 7704. There are 24 integers that are factors of 7704. The greatest factor of 7704 is 7704.

3. What are the Factors of 7712?

Answer: Factors of 7712 are 1, 2, 4, 8, 16, 32, 241, 482, 964, 1928, 3856, 7712. There are 12 integers that are factors of 7712. The greatest factor of 7712 is 7712.

4. How to Find the LCM of 7704 and 7712?

Answer:

Least Common Multiple of 7704 and 7712 = 7426656

Step 1: Find the prime factorization of 7704

7704 = 2 x 2 x 2 x 3 x 3 x 107

Step 2: Find the prime factorization of 7712

7712 = 2 x 2 x 2 x 2 x 2 x 241

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

LCM = 7426656 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 107 x 241

Step 4: Therefore, the least common multiple of 7704 and 7712 is 7426656.