Least Common Multiple of 9905 and 9912

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9905 and 9912 the smallest integer that is 14025480 that is divisible by both numbers.

Least Common Multiple (LCM) of 9905 and 9912 is 14025480.

LCM(9905,9912) = 14025480

LCM of 9905 and 9912

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

LCM of:
and

Least Common Multiple of 9905 and 9912

LCM of 9905 and 9912 is 14025480

Least common multiple can be found by multiplying the highest exponent prime factors of 9905 and 9912. First we will calculate the prime factors of 9905 and 9912.

Prime Factorization of 9905


5 9905
7 1981
283 283
1

Prime factors of 9905 are 5, 7,283. Prime factorization of 9905 in exponential form is:

9905 = 51×71×2831

Prime Factorization of 9912


2 9912
2 4956
2 2478
3 1239
7 413
59 59
1

Prime factors of 9912 are 2, 3, 7,59. Prime factorization of 9912 in exponential form is:

9912 = 23×31×71×591

Now multiplying the highest exponent prime factors to calculate the LCM of 9905 and 9912.

LCM(9905,9912) = 23×31×51×71×591×2831
LCM(9905,9912) = 14025480

Factors of 9905

List of positive integer factors of 9905 that divides 9905 without a remainder.

1, 5, 7, 35, 283, 1415, 1981, 9905

Factors of 9912

List of positive integer factors of 9912 that divides 9912 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 59, 84, 118, 168, 177, 236, 354, 413, 472, 708, 826, 1239, 1416, 1652, 2478, 3304, 4956, 9912

Least Common Multiple of 9905 and 9912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9905 and 9912, than apply into the LCM equation.

GCF(9905,9912) = 7
LCM(9905,9912) = ( 9905 × 9912) / 7
LCM(9905,9912) = 98178360 / 7
LCM(9905,9912) = 14025480

Properties of LCM 9905 and 9912

(i) The LCM of 9912 and 9905 is associative

LCM of 9905 and 9912 = LCM of 9912 and 9905

Related Least Common Multiples of 9905

Related Least Common Multiples of 9912

Frequently Asked Questions on LCM of 9905 and 9912

1. What is the LCM of 9905 and 9912?

Answer: LCM of 9905 and 9912 is 14025480.

2. What are the Factors of 9905?

Answer: Factors of 9905 are 1, 5, 7, 35, 283, 1415, 1981, 9905. There are 8 integers that are factors of 9905. The greatest factor of 9905 is 9905.

3. What are the Factors of 9912?

Answer: Factors of 9912 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 59, 84, 118, 168, 177, 236, 354, 413, 472, 708, 826, 1239, 1416, 1652, 2478, 3304, 4956, 9912. There are 32 integers that are factors of 9912. The greatest factor of 9912 is 9912.

4. How to Find the LCM of 9905 and 9912?

Answer:

Least Common Multiple of 9905 and 9912 = 14025480

Step 1: Find the prime factorization of 9905

9905 = 5 x 7 x 283

Step 2: Find the prime factorization of 9912

9912 = 2 x 2 x 2 x 3 x 7 x 59

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

LCM = 14025480 = 2 x 2 x 2 x 3 x 5 x 7 x 59 x 283

Step 4: Therefore, the least common multiple of 9905 and 9912 is 14025480.