Least Common Multiple of 7008 and 7014

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7008 and 7014 the smallest integer that is 8192352 that is divisible by both numbers.

Least Common Multiple (LCM) of 7008 and 7014 is 8192352.

LCM(7008,7014) = 8192352

LCM of 7008 and 7014

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

LCM of:
and

Least Common Multiple of 7008 and 7014

LCM of 7008 and 7014 is 8192352

Least common multiple can be found by multiplying the highest exponent prime factors of 7008 and 7014. First we will calculate the prime factors of 7008 and 7014.

Prime Factorization of 7008


2 7008
2 3504
2 1752
2 876
2 438
3 219
73 73
1

Prime factors of 7008 are 2, 3,73. Prime factorization of 7008 in exponential form is:

7008 = 25×31×731

Prime Factorization of 7014


2 7014
3 3507
7 1169
167 167
1

Prime factors of 7014 are 2, 3, 7,167. Prime factorization of 7014 in exponential form is:

7014 = 21×31×71×1671

Now multiplying the highest exponent prime factors to calculate the LCM of 7008 and 7014.

LCM(7008,7014) = 25×31×71×731×1671
LCM(7008,7014) = 8192352

Factors of 7008

List of positive integer factors of 7008 that divides 7008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008

Factors of 7014

List of positive integer factors of 7014 that divides 7014 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014

Least Common Multiple of 7008 and 7014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7008 and 7014, than apply into the LCM equation.

GCF(7008,7014) = 6
LCM(7008,7014) = ( 7008 × 7014) / 6
LCM(7008,7014) = 49154112 / 6
LCM(7008,7014) = 8192352

Properties of LCM 7008 and 7014

(i) The LCM of 7014 and 7008 is associative

LCM of 7008 and 7014 = LCM of 7014 and 7008

Related Least Common Multiples of 7008

Related Least Common Multiples of 7014

Frequently Asked Questions on LCM of 7008 and 7014

1. What is the LCM of 7008 and 7014?

Answer: LCM of 7008 and 7014 is 8192352.

2. What are the Factors of 7008?

Answer: Factors of 7008 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008. There are 24 integers that are factors of 7008. The greatest factor of 7008 is 7008.

3. What are the Factors of 7014?

Answer: Factors of 7014 are 1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014. There are 16 integers that are factors of 7014. The greatest factor of 7014 is 7014.

4. How to Find the LCM of 7008 and 7014?

Answer:

Least Common Multiple of 7008 and 7014 = 8192352

Step 1: Find the prime factorization of 7008

7008 = 2 x 2 x 2 x 2 x 2 x 3 x 73

Step 2: Find the prime factorization of 7014

7014 = 2 x 3 x 7 x 167

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

LCM = 8192352 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 73 x 167

Step 4: Therefore, the least common multiple of 7008 and 7014 is 8192352.