Least Common Multiple (LCM) of 120 and 51
The least common multiple (LCM) of 120 and 51 is 2040.
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 51?
First, calculate the GCD of 120 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 51 = 2 remainder 18 |
| 2 | 51 ÷ 18 = 2 remainder 15 |
| 3 | 18 ÷ 15 = 1 remainder 3 |
| 4 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 97 | 2134 |
| 83 and 163 | 13529 |
| 187 and 15 | 2805 |
| 128 and 27 | 3456 |
| 75 and 114 | 2850 |