Least Common Multiple of 1010 and 1014

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1010 and 1014 the smallest integer that is 512070 that is divisible by both numbers.

Least Common Multiple (LCM) of 1010 and 1014 is 512070.

LCM(1010,1014) = 512070

LCM of 1010 and 1014

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

LCM of:
and

Least Common Multiple of 1010 and 1014

LCM of 1010 and 1014 is 512070

Least common multiple can be found by multiplying the highest exponent prime factors of 1010 and 1014. First we will calculate the prime factors of 1010 and 1014.

Prime Factorization of 1010


2 1010
5 505
101 101
1

Prime factors of 1010 are 2, 5,101. Prime factorization of 1010 in exponential form is:

1010 = 21×51×1011

Prime Factorization of 1014


2 1014
3 507
13 169
13 13
1

Prime factors of 1014 are 2, 3,13. Prime factorization of 1014 in exponential form is:

1014 = 21×31×132

Now multiplying the highest exponent prime factors to calculate the LCM of 1010 and 1014.

LCM(1010,1014) = 21×31×51×132×1011
LCM(1010,1014) = 512070

Factors of 1010

List of positive integer factors of 1010 that divides 1010 without a remainder.

1, 2, 5, 10, 101, 202, 505, 1010

Factors of 1014

List of positive integer factors of 1014 that divides 1014 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014

Least Common Multiple of 1010 and 1014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1010 and 1014, than apply into the LCM equation.

GCF(1010,1014) = 2
LCM(1010,1014) = ( 1010 × 1014) / 2
LCM(1010,1014) = 1024140 / 2
LCM(1010,1014) = 512070

Properties of LCM 1010 and 1014

(i) The LCM of 1014 and 1010 is associative

LCM of 1010 and 1014 = LCM of 1014 and 1010

Related Least Common Multiples of 1010

Related Least Common Multiples of 1014

Frequently Asked Questions on LCM of 1010 and 1014

1. What is the LCM of 1010 and 1014?

Answer: LCM of 1010 and 1014 is 512070.

2. What are the Factors of 1010?

Answer: Factors of 1010 are 1, 2, 5, 10, 101, 202, 505, 1010. There are 8 integers that are factors of 1010. The greatest factor of 1010 is 1010.

3. What are the Factors of 1014?

Answer: Factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014. There are 12 integers that are factors of 1014. The greatest factor of 1014 is 1014.

4. How to Find the LCM of 1010 and 1014?

Answer:

Least Common Multiple of 1010 and 1014 = 512070

Step 1: Find the prime factorization of 1010

1010 = 2 x 5 x 101

Step 2: Find the prime factorization of 1014

1014 = 2 x 3 x 13 x 13

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

LCM = 512070 = 2 x 3 x 5 x 13 x 13 x 101

Step 4: Therefore, the least common multiple of 1010 and 1014 is 512070.