Least Common Multiple of 6 and 35

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

• Least Common Multiple of 6 and 35 by Prime method
• Least Common Multiple of 6 and 35 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 35. First we will calculate the prime factors of 6 and 35.

Prime Factorization of 6

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 2¹×3¹

Prime Factorization of 35

Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:

35 = 5¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 35.

LCM(6,35) = 2¹×3¹×5¹×7¹
LCM(6,35) = 210

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1, 5, 7, 35

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 35, than apply into the LCM equation.

GCF(6,35) = 1
LCM(6,35) = ( 6 × 35) / 1
LCM(6,35) = 210 / 1
LCM(6,35) = 210

(i) The LCM of 35 and 6 is associative

LCM of 6 and 35 = LCM of 35 and 6

1. What is the LCM of 6 and 35?

Answer: LCM of 6 and 35 is 210.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

3. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. How to Find the LCM of 6 and 35?

Answer:

Least Common Multiple of 6 and 35 = 210

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 35

35 = 5 x 7

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

LCM = 210 = 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 6 and 35 is 210.