Least Common Multiple of 11 and 58

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

• Least Common Multiple of 11 and 58 by Prime method
• Least Common Multiple of 11 and 58 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 11 and 58. First we will calculate the prime factors of 11 and 58.

Prime Factorization of 11

Prime factors of 11 are 11. Prime factorization of 11 in exponential form is:

11 = 11¹

Prime Factorization of 58

Prime factors of 58 are 2,29. Prime factorization of 58 in exponential form is:

58 = 2¹×29¹

Now multiplying the highest exponent prime factors to calculate the LCM of 11 and 58.

LCM(11,58) = 2¹×11¹×29¹
LCM(11,58) = 638

Factors of 11

List of positive integer factors of 11 that divides 11 without a remainder.

1, 11

Factors of 58

List of positive integer factors of 58 that divides 58 without a remainder.

1, 2, 29, 58

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11 and 58, than apply into the LCM equation.

GCF(11,58) = 1
LCM(11,58) = ( 11 × 58) / 1
LCM(11,58) = 638 / 1
LCM(11,58) = 638

(i) The LCM of 58 and 11 is associative

LCM of 11 and 58 = LCM of 58 and 11

1. What is the LCM of 11 and 58?

Answer: LCM of 11 and 58 is 638.

2. What are the Factors of 11?

Answer: Factors of 11 are 1, 11. There are 2 integers that are factors of 11. The greatest factor of 11 is 11.

3. What are the Factors of 58?

Answer: Factors of 58 are 1, 2, 29, 58. There are 4 integers that are factors of 58. The greatest factor of 58 is 58.

4. How to Find the LCM of 11 and 58?

Answer:

Least Common Multiple of 11 and 58 = 638

Step 1: Find the prime factorization of 11

11 = 11

Step 2: Find the prime factorization of 58

58 = 2 x 29

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

LCM = 638 = 2 x 11 x 29

Step 4: Therefore, the least common multiple of 11 and 58 is 638.