Least Common Multiple of 67008 and 67014

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 67008 and 67014 the smallest integer that is 748412352 that is divisible by both numbers.

Least Common Multiple (LCM) of 67008 and 67014 is 748412352.

LCM(67008,67014) = 748412352

LCM of 67008 and 67014

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

LCM of:
and

Least Common Multiple of 67008 and 67014

LCM of 67008 and 67014 is 748412352

Least common multiple can be found by multiplying the highest exponent prime factors of 67008 and 67014. First we will calculate the prime factors of 67008 and 67014.

Prime Factorization of 67008


2 67008
2 33504
2 16752
2 8376
2 4188
2 2094
3 1047
349 349
1

Prime factors of 67008 are 2, 3,349. Prime factorization of 67008 in exponential form is:

67008 = 26×31×3491

Prime Factorization of 67014


2 67014
3 33507
3 11169
3 3723
17 1241
73 73
1

Prime factors of 67014 are 2, 3, 17,73. Prime factorization of 67014 in exponential form is:

67014 = 21×33×171×731

Now multiplying the highest exponent prime factors to calculate the LCM of 67008 and 67014.

LCM(67008,67014) = 26×33×171×731×3491
LCM(67008,67014) = 748412352

Factors of 67008

List of positive integer factors of 67008 that divides 67008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 22336, 33504, 67008

Factors of 67014

List of positive integer factors of 67014 that divides 67014 without a remainder.

1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 73, 102, 146, 153, 219, 306, 438, 459, 657, 918, 1241, 1314, 1971, 2482, 3723, 3942, 7446, 11169, 22338, 33507, 67014

Least Common Multiple of 67008 and 67014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67008 and 67014, than apply into the LCM equation.

GCF(67008,67014) = 6
LCM(67008,67014) = ( 67008 × 67014) / 6
LCM(67008,67014) = 4490474112 / 6
LCM(67008,67014) = 748412352

Properties of LCM 67008 and 67014

(i) The LCM of 67014 and 67008 is associative

LCM of 67008 and 67014 = LCM of 67014 and 67008

Related Least Common Multiples of 67008

Related Least Common Multiples of 67014

Frequently Asked Questions on LCM of 67008 and 67014

1. What is the LCM of 67008 and 67014?

Answer: LCM of 67008 and 67014 is 748412352.

2. What are the Factors of 67008?

Answer: Factors of 67008 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 22336, 33504, 67008. There are 28 integers that are factors of 67008. The greatest factor of 67008 is 67008.

3. What are the Factors of 67014?

Answer: Factors of 67014 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 73, 102, 146, 153, 219, 306, 438, 459, 657, 918, 1241, 1314, 1971, 2482, 3723, 3942, 7446, 11169, 22338, 33507, 67014. There are 32 integers that are factors of 67014. The greatest factor of 67014 is 67014.

4. How to Find the LCM of 67008 and 67014?

Answer:

Least Common Multiple of 67008 and 67014 = 748412352

Step 1: Find the prime factorization of 67008

67008 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 349

Step 2: Find the prime factorization of 67014

67014 = 2 x 3 x 3 x 3 x 17 x 73

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

LCM = 748412352 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17 x 73 x 349

Step 4: Therefore, the least common multiple of 67008 and 67014 is 748412352.