Least Common Multiple (LCM) of 120 and 43
The least common multiple (LCM) of 120 and 43 is 5160.
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 120 and 43?
First, calculate the GCD of 120 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 43 = 2 remainder 34 |
| 2 | 43 ÷ 34 = 1 remainder 9 |
| 3 | 34 ÷ 9 = 3 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 134 | 10988 |
| 134 and 187 | 25058 |
| 16 and 161 | 2576 |
| 125 and 127 | 15875 |
| 45 and 94 | 4230 |