Least Common Multiple of 67000 and 67008

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 67000 and 67008 the smallest integer that is 561192000 that is divisible by both numbers.

Least Common Multiple (LCM) of 67000 and 67008 is 561192000.

LCM(67000,67008) = 561192000

LCM of 67000 and 67008

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

LCM of:
and

Least Common Multiple of 67000 and 67008

LCM of 67000 and 67008 is 561192000

Least common multiple can be found by multiplying the highest exponent prime factors of 67000 and 67008. First we will calculate the prime factors of 67000 and 67008.

Prime Factorization of 67000


2 67000
2 33500
2 16750
5 8375
5 1675
5 335
67 67
1

Prime factors of 67000 are 2, 5,67. Prime factorization of 67000 in exponential form is:

67000 = 23×53×671

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

Now multiplying the highest exponent prime factors to calculate the LCM of 67000 and 67008.

LCM(67000,67008) = 26×31×53×671×3491
LCM(67000,67008) = 561192000

Factors of 67000

List of positive integer factors of 67000 that divides 67000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 125, 134, 200, 250, 268, 335, 500, 536, 670, 1000, 1340, 1675, 2680, 3350, 6700, 8375, 13400, 16750, 33500, 67000

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

Least Common Multiple of 67000 and 67008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67000 and 67008, than apply into the LCM equation.

GCF(67000,67008) = 8
LCM(67000,67008) = ( 67000 × 67008) / 8
LCM(67000,67008) = 4489536000 / 8
LCM(67000,67008) = 561192000

Properties of LCM 67000 and 67008

(i) The LCM of 67008 and 67000 is associative

LCM of 67000 and 67008 = LCM of 67008 and 67000

Related Least Common Multiples of 67000

Related Least Common Multiples of 67008

Frequently Asked Questions on LCM of 67000 and 67008

1. What is the LCM of 67000 and 67008?

Answer: LCM of 67000 and 67008 is 561192000.

2. What are the Factors of 67000?

Answer: Factors of 67000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 125, 134, 200, 250, 268, 335, 500, 536, 670, 1000, 1340, 1675, 2680, 3350, 6700, 8375, 13400, 16750, 33500, 67000. There are 32 integers that are factors of 67000. The greatest factor of 67000 is 67000.

3. 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.

4. How to Find the LCM of 67000 and 67008?

Answer:

Least Common Multiple of 67000 and 67008 = 561192000

Step 1: Find the prime factorization of 67000

67000 = 2 x 2 x 2 x 5 x 5 x 5 x 67

Step 2: Find the prime factorization of 67008

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

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

LCM = 561192000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 67 x 349

Step 4: Therefore, the least common multiple of 67000 and 67008 is 561192000.