Least Common Multiple (LCM) of 120 and 74
The least common multiple (LCM) of 120 and 74 is 4440.
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 74?
First, calculate the GCD of 120 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 74 = 1 remainder 46 |
| 2 | 74 ÷ 46 = 1 remainder 28 |
| 3 | 46 ÷ 28 = 1 remainder 18 |
| 4 | 28 ÷ 18 = 1 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 165 | 24090 |
| 158 and 89 | 14062 |
| 151 and 160 | 24160 |
| 132 and 186 | 4092 |
| 186 and 115 | 21390 |