Least Common Multiple (LCM) of 100 and 43
The least common multiple (LCM) of 100 and 43 is 4300.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 100 and 43?
First, calculate the GCD of 100 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 43 = 2 remainder 14 |
| 2 | 43 ÷ 14 = 3 remainder 1 |
| 3 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 117 | 4095 |
| 122 and 192 | 11712 |
| 115 and 144 | 16560 |
| 20 and 96 | 480 |
| 57 and 113 | 6441 |