Least Common Multiple of 59 and 58

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

• Least Common Multiple of 59 and 58 by Prime method
• Least Common Multiple of 59 and 58 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 59 and 58. First we will calculate the prime factors of 59 and 58.

Prime Factorization of 59

Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:

59 = 59¹

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 59 and 58.

LCM(59,58) = 2¹×29¹×59¹
LCM(59,58) = 3422

Factors of 59

List of positive integer factors of 59 that divides 59 without a remainder.

1, 59

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 59 and 58, than apply into the LCM equation.

GCF(59,58) = 1
LCM(59,58) = ( 59 × 58) / 1
LCM(59,58) = 3422 / 1
LCM(59,58) = 3422

(i) The LCM of 58 and 59 is associative

LCM of 59 and 58 = LCM of 58 and 59

1. What is the LCM of 59 and 58?

Answer: LCM of 59 and 58 is 3422.

2. What are the Factors of 59?

Answer: Factors of 59 are 1, 59. There are 2 integers that are factors of 59. The greatest factor of 59 is 59.

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 59 and 58?

Answer:

Least Common Multiple of 59 and 58 = 3422

Step 1: Find the prime factorization of 59

59 = 59

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 = 3422 = 2 x 29 x 59

Step 4: Therefore, the least common multiple of 59 and 58 is 3422.