Least Common Multiple of 35 and 49

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

• Least Common Multiple of 35 and 49 by Prime method
• Least Common Multiple of 35 and 49 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 35 and 49. First we will calculate the prime factors of 35 and 49.

Prime Factorization of 35

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

35 = 5¹×7¹

Prime Factorization of 49

Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:

49 = 7²

Now multiplying the highest exponent prime factors to calculate the LCM of 35 and 49.

LCM(35,49) = 5¹×7²
LCM(35,49) = 245

Factors of 35

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

1, 5, 7, 35

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1, 7, 49

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35 and 49, than apply into the LCM equation.

GCF(35,49) = 7
LCM(35,49) = ( 35 × 49) / 7
LCM(35,49) = 1715 / 7
LCM(35,49) = 245

(i) The LCM of 49 and 35 is associative

LCM of 35 and 49 = LCM of 49 and 35

1. What is the LCM of 35 and 49?

Answer: LCM of 35 and 49 is 245.

2. 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.

3. What are the Factors of 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

4. How to Find the LCM of 35 and 49?

Answer:

Least Common Multiple of 35 and 49 = 245

Step 1: Find the prime factorization of 35

35 = 5 x 7

Step 2: Find the prime factorization of 49

49 = 7 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 = 245 = 5 x 7 x 7

Step 4: Therefore, the least common multiple of 35 and 49 is 245.