Least Common Multiple (LCM) of 76 and 120
The least common multiple (LCM) of 76 and 120 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 76 and 120?
First, calculate the GCD of 76 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 120 = 0 remainder 76 |
| 2 | 120 ÷ 76 = 1 remainder 44 |
| 3 | 76 ÷ 44 = 1 remainder 32 |
| 4 | 44 ÷ 32 = 1 remainder 12 |
| 5 | 32 ÷ 12 = 2 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 100 | 1900 |
| 13 and 135 | 1755 |
| 167 and 96 | 16032 |
| 160 and 147 | 23520 |
| 145 and 60 | 1740 |