Least Common Multiple (LCM) of 120 and 69
The least common multiple (LCM) of 120 and 69 is 2760.
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 69?
First, calculate the GCD of 120 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 69 = 1 remainder 51 |
| 2 | 69 ÷ 51 = 1 remainder 18 |
| 3 | 51 ÷ 18 = 2 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 75 | 4575 |
| 16 and 184 | 368 |
| 134 and 111 | 14874 |
| 64 and 17 | 1088 |
| 68 and 177 | 12036 |