Least Common Multiple of 43 and 46

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

• Least Common Multiple of 43 and 46 by Prime method
• Least Common Multiple of 43 and 46 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 43 and 46. First we will calculate the prime factors of 43 and 46.

Prime Factorization of 43

Prime factors of 43 are 43. Prime factorization of 43 in exponential form is:

43 = 43¹

Prime Factorization of 46

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

46 = 2¹×23¹

Now multiplying the highest exponent prime factors to calculate the LCM of 43 and 46.

LCM(43,46) = 2¹×23¹×43¹
LCM(43,46) = 1978

Factors of 43

List of positive integer factors of 43 that divides 43 without a remainder.

1, 43

Factors of 46

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

1, 2, 23, 46

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43 and 46, than apply into the LCM equation.

GCF(43,46) = 1
LCM(43,46) = ( 43 × 46) / 1
LCM(43,46) = 1978 / 1
LCM(43,46) = 1978

(i) The LCM of 46 and 43 is associative

LCM of 43 and 46 = LCM of 46 and 43

1. What is the LCM of 43 and 46?

Answer: LCM of 43 and 46 is 1978.

2. What are the Factors of 43?

Answer: Factors of 43 are 1, 43. There are 2 integers that are factors of 43. The greatest factor of 43 is 43.

3. 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.

4. How to Find the LCM of 43 and 46?

Answer:

Least Common Multiple of 43 and 46 = 1978

Step 1: Find the prime factorization of 43

43 = 43

Step 2: Find the prime factorization of 46

46 = 2 x 23

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

LCM = 1978 = 2 x 23 x 43

Step 4: Therefore, the least common multiple of 43 and 46 is 1978.