Least Common Multiple of 53 and 58

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

• Least Common Multiple of 53 and 58 by Prime method
• Least Common Multiple of 53 and 58 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 53 and 58. First we will calculate the prime factors of 53 and 58.

Prime Factorization of 53

Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:

53 = 53¹

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 53 and 58.

LCM(53,58) = 2¹×29¹×53¹
LCM(53,58) = 3074

Factors of 53

List of positive integer factors of 53 that divides 53 without a remainder.

1, 53

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 53 and 58, than apply into the LCM equation.

GCF(53,58) = 1
LCM(53,58) = ( 53 × 58) / 1
LCM(53,58) = 3074 / 1
LCM(53,58) = 3074

(i) The LCM of 58 and 53 is associative

LCM of 53 and 58 = LCM of 58 and 53

1. What is the LCM of 53 and 58?

Answer: LCM of 53 and 58 is 3074.

2. What are the Factors of 53?

Answer: Factors of 53 are 1, 53. There are 2 integers that are factors of 53. The greatest factor of 53 is 53.

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 53 and 58?

Answer:

Least Common Multiple of 53 and 58 = 3074

Step 1: Find the prime factorization of 53

53 = 53

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 = 3074 = 2 x 29 x 53

Step 4: Therefore, the least common multiple of 53 and 58 is 3074.