Least Common Multiple of 27001 and 27006

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

• Least Common Multiple of 27001 and 27006 by Prime method
• Least Common Multiple of 27001 and 27006 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 27001 and 27006. First we will calculate the prime factors of 27001 and 27006.

Prime Factorization of 27001

Prime factors of 27001 are 13, 31,67. Prime factorization of 27001 in exponential form is:

27001 = 13¹×31¹×67¹

Prime Factorization of 27006

Prime factors of 27006 are 2, 3, 7,643. Prime factorization of 27006 in exponential form is:

27006 = 2¹×3¹×7¹×643¹

Now multiplying the highest exponent prime factors to calculate the LCM of 27001 and 27006.

LCM(27001,27006) = 2¹×3¹×7¹×13¹×31¹×67¹×643¹
LCM(27001,27006) = 729189006

Factors of 27001

List of positive integer factors of 27001 that divides 27001 without a remainder.

1, 13, 31, 67, 403, 871, 2077, 27001

Factors of 27006

List of positive integer factors of 27006 that divides 27006 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 643, 1286, 1929, 3858, 4501, 9002, 13503, 27006

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27001 and 27006, than apply into the LCM equation.

GCF(27001,27006) = 1
LCM(27001,27006) = ( 27001 × 27006) / 1
LCM(27001,27006) = 729189006 / 1
LCM(27001,27006) = 729189006

(i) The LCM of 27006 and 27001 is associative

LCM of 27001 and 27006 = LCM of 27006 and 27001

1. What is the LCM of 27001 and 27006?

Answer: LCM of 27001 and 27006 is 729189006.

2. What are the Factors of 27001?

Answer: Factors of 27001 are 1, 13, 31, 67, 403, 871, 2077, 27001. There are 8 integers that are factors of 27001. The greatest factor of 27001 is 27001.

3. What are the Factors of 27006?

Answer: Factors of 27006 are 1, 2, 3, 6, 7, 14, 21, 42, 643, 1286, 1929, 3858, 4501, 9002, 13503, 27006. There are 16 integers that are factors of 27006. The greatest factor of 27006 is 27006.

4. How to Find the LCM of 27001 and 27006?

Answer:

Least Common Multiple of 27001 and 27006 = 729189006

Step 1: Find the prime factorization of 27001

27001 = 13 x 31 x 67

Step 2: Find the prime factorization of 27006

27006 = 2 x 3 x 7 x 643

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

LCM = 729189006 = 2 x 3 x 7 x 13 x 31 x 67 x 643

Step 4: Therefore, the least common multiple of 27001 and 27006 is 729189006.