Least Common Multiple of 10010 and 10014

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10010 and 10014 the smallest integer that is 50120070 that is divisible by both numbers.

Least Common Multiple (LCM) of 10010 and 10014 is 50120070.

LCM(10010,10014) = 50120070

LCM of 10010 and 10014

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

LCM of:
and

Least Common Multiple of 10010 and 10014

LCM of 10010 and 10014 is 50120070

Least common multiple can be found by multiplying the highest exponent prime factors of 10010 and 10014. First we will calculate the prime factors of 10010 and 10014.

Prime Factorization of 10010


2 10010
5 5005
7 1001
11 143
13 13
1

Prime factors of 10010 are 2, 5, 7, 11,13. Prime factorization of 10010 in exponential form is:

10010 = 21×51×71×111×131

Prime Factorization of 10014


2 10014
3 5007
1669 1669
1

Prime factors of 10014 are 2, 3,1669. Prime factorization of 10014 in exponential form is:

10014 = 21×31×16691

Now multiplying the highest exponent prime factors to calculate the LCM of 10010 and 10014.

LCM(10010,10014) = 21×31×51×71×111×131×16691
LCM(10010,10014) = 50120070

Factors of 10010

List of positive integer factors of 10010 that divides 10010 without a remainder.

1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010

Factors of 10014

List of positive integer factors of 10014 that divides 10014 without a remainder.

1, 2, 3, 6, 1669, 3338, 5007, 10014

Least Common Multiple of 10010 and 10014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10010 and 10014, than apply into the LCM equation.

GCF(10010,10014) = 2
LCM(10010,10014) = ( 10010 × 10014) / 2
LCM(10010,10014) = 100240140 / 2
LCM(10010,10014) = 50120070

Properties of LCM 10010 and 10014

(i) The LCM of 10014 and 10010 is associative

LCM of 10010 and 10014 = LCM of 10014 and 10010

Related Least Common Multiples of 10010

Related Least Common Multiples of 10014

Frequently Asked Questions on LCM of 10010 and 10014

1. What is the LCM of 10010 and 10014?

Answer: LCM of 10010 and 10014 is 50120070.

2. What are the Factors of 10010?

Answer: Factors of 10010 are 1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010. There are 32 integers that are factors of 10010. The greatest factor of 10010 is 10010.

3. What are the Factors of 10014?

Answer: Factors of 10014 are 1, 2, 3, 6, 1669, 3338, 5007, 10014. There are 8 integers that are factors of 10014. The greatest factor of 10014 is 10014.

4. How to Find the LCM of 10010 and 10014?

Answer:

Least Common Multiple of 10010 and 10014 = 50120070

Step 1: Find the prime factorization of 10010

10010 = 2 x 5 x 7 x 11 x 13

Step 2: Find the prime factorization of 10014

10014 = 2 x 3 x 1669

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

LCM = 50120070 = 2 x 3 x 5 x 7 x 11 x 13 x 1669

Step 4: Therefore, the least common multiple of 10010 and 10014 is 50120070.