Least Common Multiple (LCM) of 120 and 46
The least common multiple (LCM) of 120 and 46 is 2760.
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 46?
First, calculate the GCD of 120 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 46 = 2 remainder 28 |
| 2 | 46 ÷ 28 = 1 remainder 18 |
| 3 | 28 ÷ 18 = 1 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 131 | 5895 |
| 123 and 12 | 492 |
| 80 and 12 | 240 |
| 62 and 167 | 10354 |
| 75 and 118 | 8850 |