Least Common Multiple (LCM) of 120 and 196
The least common multiple (LCM) of 120 and 196 is 5880.
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 196?
First, calculate the GCD of 120 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 196 = 0 remainder 120 |
| 2 | 196 ÷ 120 = 1 remainder 76 |
| 3 | 120 ÷ 76 = 1 remainder 44 |
| 4 | 76 ÷ 44 = 1 remainder 32 |
| 5 | 44 ÷ 32 = 1 remainder 12 |
| 6 | 32 ÷ 12 = 2 remainder 8 |
| 7 | 12 ÷ 8 = 1 remainder 4 |
| 8 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 157 | 24021 |
| 125 and 177 | 22125 |
| 129 and 163 | 21027 |
| 169 and 78 | 1014 |
| 51 and 186 | 3162 |