Least Common Multiple (LCM) of 120 and 151
The least common multiple (LCM) of 120 and 151 is 18120.
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 151?
First, calculate the GCD of 120 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 151 = 0 remainder 120 |
| 2 | 151 ÷ 120 = 1 remainder 31 |
| 3 | 120 ÷ 31 = 3 remainder 27 |
| 4 | 31 ÷ 27 = 1 remainder 4 |
| 5 | 27 ÷ 4 = 6 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 107 | 2140 |
| 32 and 107 | 3424 |
| 180 and 30 | 180 |
| 191 and 51 | 9741 |
| 60 and 139 | 8340 |