Least Common Multiple of 46 and 53

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

• Least Common Multiple of 46 and 53 by Prime method
• Least Common Multiple of 46 and 53 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 46 and 53. First we will calculate the prime factors of 46 and 53.

Prime Factorization of 46

Prime factors of 46 are 2,23. Prime factorization of 46 in exponential form is:

46 = 2¹×23¹

Prime Factorization of 53

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

53 = 53¹

Now multiplying the highest exponent prime factors to calculate the LCM of 46 and 53.

LCM(46,53) = 2¹×23¹×53¹
LCM(46,53) = 2438

Factors of 46

List of positive integer factors of 46 that divides 46 without a remainder.

1, 2, 23, 46

Factors of 53

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

1, 53

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46 and 53, than apply into the LCM equation.

GCF(46,53) = 1
LCM(46,53) = ( 46 × 53) / 1
LCM(46,53) = 2438 / 1
LCM(46,53) = 2438

(i) The LCM of 53 and 46 is associative

LCM of 46 and 53 = LCM of 53 and 46

1. What is the LCM of 46 and 53?

Answer: LCM of 46 and 53 is 2438.

2. What are the Factors of 46?

Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.

3. 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.

4. How to Find the LCM of 46 and 53?

Answer:

Least Common Multiple of 46 and 53 = 2438

Step 1: Find the prime factorization of 46

46 = 2 x 23

Step 2: Find the prime factorization of 53

53 = 53

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

LCM = 2438 = 2 x 23 x 53

Step 4: Therefore, the least common multiple of 46 and 53 is 2438.