Least Common Multiple of 13065 and 13070

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

• Least Common Multiple of 13065 and 13070 by Prime method
• Least Common Multiple of 13065 and 13070 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 13065 and 13070. First we will calculate the prime factors of 13065 and 13070.

Prime Factorization of 13065

Prime factors of 13065 are 3, 5, 13,67. Prime factorization of 13065 in exponential form is:

13065 = 3¹×5¹×13¹×67¹

Prime Factorization of 13070

Prime factors of 13070 are 2, 5,1307. Prime factorization of 13070 in exponential form is:

13070 = 2¹×5¹×1307¹

Now multiplying the highest exponent prime factors to calculate the LCM of 13065 and 13070.

LCM(13065,13070) = 2¹×3¹×5¹×13¹×67¹×1307¹
LCM(13065,13070) = 34151910

Factors of 13065

List of positive integer factors of 13065 that divides 13065 without a remainder.

1, 3, 5, 13, 15, 39, 65, 67, 195, 201, 335, 871, 1005, 2613, 4355, 13065

Factors of 13070

List of positive integer factors of 13070 that divides 13070 without a remainder.

1, 2, 5, 10, 1307, 2614, 6535, 13070

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13065 and 13070, than apply into the LCM equation.

GCF(13065,13070) = 5
LCM(13065,13070) = ( 13065 × 13070) / 5
LCM(13065,13070) = 170759550 / 5
LCM(13065,13070) = 34151910

(i) The LCM of 13070 and 13065 is associative

LCM of 13065 and 13070 = LCM of 13070 and 13065

1. What is the LCM of 13065 and 13070?

Answer: LCM of 13065 and 13070 is 34151910.

2. What are the Factors of 13065?

Answer: Factors of 13065 are 1, 3, 5, 13, 15, 39, 65, 67, 195, 201, 335, 871, 1005, 2613, 4355, 13065. There are 16 integers that are factors of 13065. The greatest factor of 13065 is 13065.

3. What are the Factors of 13070?

Answer: Factors of 13070 are 1, 2, 5, 10, 1307, 2614, 6535, 13070. There are 8 integers that are factors of 13070. The greatest factor of 13070 is 13070.

4. How to Find the LCM of 13065 and 13070?

Answer:

Least Common Multiple of 13065 and 13070 = 34151910

Step 1: Find the prime factorization of 13065

13065 = 3 x 5 x 13 x 67

Step 2: Find the prime factorization of 13070

13070 = 2 x 5 x 1307

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

LCM = 34151910 = 2 x 3 x 5 x 13 x 67 x 1307

Step 4: Therefore, the least common multiple of 13065 and 13070 is 34151910.