Least Common Multiple (LCM) of 120 and 76
The least common multiple (LCM) of 120 and 76 is 2280.
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 76?
First, calculate the GCD of 120 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 76 = 1 remainder 44 |
| 2 | 76 ÷ 44 = 1 remainder 32 |
| 3 | 44 ÷ 32 = 1 remainder 12 |
| 4 | 32 ÷ 12 = 2 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 127 | 20320 |
| 153 and 111 | 5661 |
| 148 and 195 | 28860 |
| 18 and 35 | 630 |
| 129 and 34 | 4386 |