Least Common Multiple (LCM) of 120 and 78
The least common multiple (LCM) of 120 and 78 is 1560.
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 78?
First, calculate the GCD of 120 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 78 = 1 remainder 42 |
| 2 | 78 ÷ 42 = 1 remainder 36 |
| 3 | 42 ÷ 36 = 1 remainder 6 |
| 4 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 34 | 5950 |
| 120 and 102 | 2040 |
| 123 and 81 | 3321 |
| 127 and 112 | 14224 |
| 29 and 108 | 3132 |