Least Common Multiple of 67001 and 67005

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

• Least Common Multiple of 67001 and 67005 by Prime method
• Least Common Multiple of 67001 and 67005 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67001 and 67005. First we will calculate the prime factors of 67001 and 67005.

Prime Factorization of 67001

Prime factors of 67001 are 11,6091. Prime factorization of 67001 in exponential form is:

67001 = 11¹×6091¹

Prime Factorization of 67005

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

67005 = 3²×5¹×1489¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67001 and 67005.

LCM(67001,67005) = 3²×5¹×11¹×1489¹×6091¹
LCM(67001,67005) = 4489402005

Factors of 67001

List of positive integer factors of 67001 that divides 67001 without a remainder.

1, 11, 6091, 67001

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

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67001 and 67005, than apply into the LCM equation.

GCF(67001,67005) = 1
LCM(67001,67005) = ( 67001 × 67005) / 1
LCM(67001,67005) = 4489402005 / 1
LCM(67001,67005) = 4489402005

(i) The LCM of 67005 and 67001 is associative

LCM of 67001 and 67005 = LCM of 67005 and 67001

1. What is the LCM of 67001 and 67005?

Answer: LCM of 67001 and 67005 is 4489402005.

2. What are the Factors of 67001?

Answer: Factors of 67001 are 1, 11, 6091, 67001. There are 4 integers that are factors of 67001. The greatest factor of 67001 is 67001.

3. 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.

4. How to Find the LCM of 67001 and 67005?

Answer:

Least Common Multiple of 67001 and 67005 = 4489402005

Step 1: Find the prime factorization of 67001

67001 = 11 x 6091

Step 2: Find the prime factorization of 67005

67005 = 3 x 3 x 5 x 1489

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

LCM = 4489402005 = 3 x 3 x 5 x 11 x 1489 x 6091

Step 4: Therefore, the least common multiple of 67001 and 67005 is 4489402005.