Least Common Multiple of 67000 and 67002

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 67002 the smallest integer that is 2244567000 that is divisible by both numbers.

Least Common Multiple (LCM) of 67000 and 67002 is 2244567000.

LCM(67000,67002) = 2244567000

LCM of 67000 and 67002

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

LCM of:
and

Least Common Multiple of 67000 and 67002

LCM of 67000 and 67002 is 2244567000

Least common multiple can be found by multiplying the highest exponent prime factors of 67000 and 67002. First we will calculate the prime factors of 67000 and 67002.

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 67002


2 67002
3 33501
13 11167
859 859
1

Prime factors of 67002 are 2, 3, 13,859. Prime factorization of 67002 in exponential form is:

67002 = 21×31×131×8591

Now multiplying the highest exponent prime factors to calculate the LCM of 67000 and 67002.

LCM(67000,67002) = 23×31×53×131×671×8591
LCM(67000,67002) = 2244567000

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 67002

List of positive integer factors of 67002 that divides 67002 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 859, 1718, 2577, 5154, 11167, 22334, 33501, 67002

Least Common Multiple of 67000 and 67002 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 67002, than apply into the LCM equation.

GCF(67000,67002) = 2
LCM(67000,67002) = ( 67000 × 67002) / 2
LCM(67000,67002) = 4489134000 / 2
LCM(67000,67002) = 2244567000

Properties of LCM 67000 and 67002

(i) The LCM of 67002 and 67000 is associative

LCM of 67000 and 67002 = LCM of 67002 and 67000

Related Least Common Multiples of 67000

Related Least Common Multiples of 67002

Frequently Asked Questions on LCM of 67000 and 67002

1. What is the LCM of 67000 and 67002?

Answer: LCM of 67000 and 67002 is 2244567000.

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 67002?

Answer: Factors of 67002 are 1, 2, 3, 6, 13, 26, 39, 78, 859, 1718, 2577, 5154, 11167, 22334, 33501, 67002. There are 16 integers that are factors of 67002. The greatest factor of 67002 is 67002.

4. How to Find the LCM of 67000 and 67002?

Answer:

Least Common Multiple of 67000 and 67002 = 2244567000

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 67002

67002 = 2 x 3 x 13 x 859

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

LCM = 2244567000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 13 x 67 x 859

Step 4: Therefore, the least common multiple of 67000 and 67002 is 2244567000.