Least Common Multiple (LCM) of 120 and 73
The least common multiple (LCM) of 120 and 73 is 8760.
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 73?
First, calculate the GCD of 120 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 73 = 1 remainder 47 |
| 2 | 73 ÷ 47 = 1 remainder 26 |
| 3 | 47 ÷ 26 = 1 remainder 21 |
| 4 | 26 ÷ 21 = 1 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 14 | 378 |
| 64 and 63 | 4032 |
| 187 and 97 | 18139 |
| 49 and 80 | 3920 |
| 114 and 33 | 1254 |