Least Common Multiple (LCM) of 196 and 120
The least common multiple (LCM) of 196 and 120 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 196 and 120?
First, calculate the GCD of 196 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 120 = 1 remainder 76 |
| 2 | 120 ÷ 76 = 1 remainder 44 |
| 3 | 76 ÷ 44 = 1 remainder 32 |
| 4 | 44 ÷ 32 = 1 remainder 12 |
| 5 | 32 ÷ 12 = 2 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 122 | 6466 |
| 40 and 11 | 440 |
| 37 and 178 | 6586 |
| 38 and 15 | 570 |
| 114 and 85 | 9690 |