Least Common Multiple of 67005 and 67012

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

• Least Common Multiple of 67005 and 67012 by Prime method
• Least Common Multiple of 67005 and 67012 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67005 and 67012. First we will calculate the prime factors of 67005 and 67012.

Prime Factorization of 67005

Prime factors of 67005 are 3, 5,1489. Prime factorization of 67005 in exponential form is:

67005 = 3²×5¹×1489¹

Prime Factorization of 67012

Prime factors of 67012 are 2, 11,1523. Prime factorization of 67012 in exponential form is:

67012 = 2²×11¹×1523¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67005 and 67012.

LCM(67005,67012) = 2²×3²×5¹×11¹×1489¹×1523¹
LCM(67005,67012) = 4490139060

Factors of 67005

List of positive integer factors of 67005 that divides 67005 without a remainder.

1, 3, 5, 9, 15, 45, 1489, 4467, 7445, 13401, 22335, 67005

Factors of 67012

List of positive integer factors of 67012 that divides 67012 without a remainder.

1, 2, 4, 11, 22, 44, 1523, 3046, 6092, 16753, 33506, 67012

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67005 and 67012, than apply into the LCM equation.

GCF(67005,67012) = 1
LCM(67005,67012) = ( 67005 × 67012) / 1
LCM(67005,67012) = 4490139060 / 1
LCM(67005,67012) = 4490139060

(i) The LCM of 67012 and 67005 is associative

LCM of 67005 and 67012 = LCM of 67012 and 67005

1. What is the LCM of 67005 and 67012?

Answer: LCM of 67005 and 67012 is 4490139060.

2. What are the Factors of 67005?

Answer: Factors of 67005 are 1, 3, 5, 9, 15, 45, 1489, 4467, 7445, 13401, 22335, 67005. There are 12 integers that are factors of 67005. The greatest factor of 67005 is 67005.

3. What are the Factors of 67012?

Answer: Factors of 67012 are 1, 2, 4, 11, 22, 44, 1523, 3046, 6092, 16753, 33506, 67012. There are 12 integers that are factors of 67012. The greatest factor of 67012 is 67012.

4. How to Find the LCM of 67005 and 67012?

Answer:

Least Common Multiple of 67005 and 67012 = 4490139060

Step 1: Find the prime factorization of 67005

67005 = 3 x 3 x 5 x 1489

Step 2: Find the prime factorization of 67012

67012 = 2 x 2 x 11 x 1523

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

LCM = 4490139060 = 2 x 2 x 3 x 3 x 5 x 11 x 1489 x 1523

Step 4: Therefore, the least common multiple of 67005 and 67012 is 4490139060.