Least Common Multiple of 27005 and 27006

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

• Least Common Multiple of 27005 and 27006 by Prime method
• Least Common Multiple of 27005 and 27006 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 27005 and 27006. First we will calculate the prime factors of 27005 and 27006.

Prime Factorization of 27005

Prime factors of 27005 are 5, 11,491. Prime factorization of 27005 in exponential form is:

27005 = 5¹×11¹×491¹

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 27005 and 27006.

LCM(27005,27006) = 2¹×3¹×5¹×7¹×11¹×491¹×643¹
LCM(27005,27006) = 729297030

Factors of 27005

List of positive integer factors of 27005 that divides 27005 without a remainder.

1, 5, 11, 55, 491, 2455, 5401, 27005

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 27005 and 27006, than apply into the LCM equation.

GCF(27005,27006) = 1
LCM(27005,27006) = ( 27005 × 27006) / 1
LCM(27005,27006) = 729297030 / 1
LCM(27005,27006) = 729297030

(i) The LCM of 27006 and 27005 is associative

LCM of 27005 and 27006 = LCM of 27006 and 27005

1. What is the LCM of 27005 and 27006?

Answer: LCM of 27005 and 27006 is 729297030.

2. What are the Factors of 27005?

Answer: Factors of 27005 are 1, 5, 11, 55, 491, 2455, 5401, 27005. There are 8 integers that are factors of 27005. The greatest factor of 27005 is 27005.

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 27005 and 27006?

Answer:

Least Common Multiple of 27005 and 27006 = 729297030

Step 1: Find the prime factorization of 27005

27005 = 5 x 11 x 491

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 = 729297030 = 2 x 3 x 5 x 7 x 11 x 491 x 643

Step 4: Therefore, the least common multiple of 27005 and 27006 is 729297030.