Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 28 and 43 the smallest integer that is 1204 that is divisible by both numbers.
Least Common Multiple (LCM) of 28 and 43 is 1204.
LCM(28,43) = 1204
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 28 and 43. First we will calculate the prime factors of 28 and 43.
Prime Factorization of 28
2 | 28 |
2 | 14 |
7 | 7 |
1 |
Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:
28 = 22×71
Prime Factorization of 43
43 | 43 |
1 |
Prime factors of 43 are 43. Prime factorization of 43 in exponential form is:
43 = 431
Now multiplying the highest exponent prime factors to calculate the LCM of 28 and 43.
LCM(28,43) = 22×71×431
LCM(28,43) = 1204
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1, 2, 4, 7, 14, 28
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1, 43
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28 and 43, than apply into the LCM equation.
GCF(28,43) = 1
LCM(28,43) = ( 28 × 43) / 1
LCM(28,43) = 1204 / 1
LCM(28,43) = 1204
(i) The LCM of 43 and 28 is associative
LCM of 28 and 43 = LCM of 43 and 28
1. What is the LCM of 28 and 43?
Answer: LCM of 28 and 43 is 1204.
2. What are the Factors of 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
3. 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.
4. How to Find the LCM of 28 and 43?
Answer:
Least Common Multiple of 28 and 43 = 1204
Step 1: Find the prime factorization of 28
28 = 2 x 2 x 7
Step 2: Find the prime factorization of 43
43 = 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1204 = 2 x 2 x 7 x 43
Step 4: Therefore, the least common multiple of 28 and 43 is 1204.