Least Common Multiple (LCM) of 43 and 118
The least common multiple (LCM) of 43 and 118 is 5074.
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 43 and 118?
First, calculate the GCD of 43 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 118 = 0 remainder 43 |
| 2 | 118 ÷ 43 = 2 remainder 32 |
| 3 | 43 ÷ 32 = 1 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 160 | 3360 |
| 84 and 134 | 5628 |
| 180 and 75 | 900 |
| 30 and 180 | 180 |
| 129 and 189 | 8127 |