Least Common Multiple of 7890 and 7896

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7890 and 7896 the smallest integer that is 10383240 that is divisible by both numbers.

Least Common Multiple (LCM) of 7890 and 7896 is 10383240.

LCM(7890,7896) = 10383240

LCM of 7890 and 7896

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

LCM of:
and

Least Common Multiple of 7890 and 7896

LCM of 7890 and 7896 is 10383240

Least common multiple can be found by multiplying the highest exponent prime factors of 7890 and 7896. First we will calculate the prime factors of 7890 and 7896.

Prime Factorization of 7890


2 7890
3 3945
5 1315
263 263
1

Prime factors of 7890 are 2, 3, 5,263. Prime factorization of 7890 in exponential form is:

7890 = 21×31×51×2631

Prime Factorization of 7896


2 7896
2 3948
2 1974
3 987
7 329
47 47
1

Prime factors of 7896 are 2, 3, 7,47. Prime factorization of 7896 in exponential form is:

7896 = 23×31×71×471

Now multiplying the highest exponent prime factors to calculate the LCM of 7890 and 7896.

LCM(7890,7896) = 23×31×51×71×471×2631
LCM(7890,7896) = 10383240

Factors of 7890

List of positive integer factors of 7890 that divides 7890 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 263, 526, 789, 1315, 1578, 2630, 3945, 7890

Factors of 7896

List of positive integer factors of 7896 that divides 7896 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 47, 56, 84, 94, 141, 168, 188, 282, 329, 376, 564, 658, 987, 1128, 1316, 1974, 2632, 3948, 7896

Least Common Multiple of 7890 and 7896 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7890 and 7896, than apply into the LCM equation.

GCF(7890,7896) = 6
LCM(7890,7896) = ( 7890 × 7896) / 6
LCM(7890,7896) = 62299440 / 6
LCM(7890,7896) = 10383240

Properties of LCM 7890 and 7896

(i) The LCM of 7896 and 7890 is associative

LCM of 7890 and 7896 = LCM of 7896 and 7890

Related Least Common Multiples of 7890

Related Least Common Multiples of 7896

Frequently Asked Questions on LCM of 7890 and 7896

1. What is the LCM of 7890 and 7896?

Answer: LCM of 7890 and 7896 is 10383240.

2. What are the Factors of 7890?

Answer: Factors of 7890 are 1, 2, 3, 5, 6, 10, 15, 30, 263, 526, 789, 1315, 1578, 2630, 3945, 7890. There are 16 integers that are factors of 7890. The greatest factor of 7890 is 7890.

3. What are the Factors of 7896?

Answer: Factors of 7896 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 47, 56, 84, 94, 141, 168, 188, 282, 329, 376, 564, 658, 987, 1128, 1316, 1974, 2632, 3948, 7896. There are 32 integers that are factors of 7896. The greatest factor of 7896 is 7896.

4. How to Find the LCM of 7890 and 7896?

Answer:

Least Common Multiple of 7890 and 7896 = 10383240

Step 1: Find the prime factorization of 7890

7890 = 2 x 3 x 5 x 263

Step 2: Find the prime factorization of 7896

7896 = 2 x 2 x 2 x 3 x 7 x 47

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

LCM = 10383240 = 2 x 2 x 2 x 3 x 5 x 7 x 47 x 263

Step 4: Therefore, the least common multiple of 7890 and 7896 is 10383240.