Least Common Multiple (LCM) of 120 and 30
The least common multiple (LCM) of 120 and 30 is 120.
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 30?
First, calculate the GCD of 120 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 30 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 141 | 8178 |
| 184 and 129 | 23736 |
| 103 and 71 | 7313 |
| 151 and 125 | 18875 |
| 40 and 48 | 240 |