Least Common Multiple (LCM) of 51 and 196
The least common multiple (LCM) of 51 and 196 is 9996.
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 51 and 196?
First, calculate the GCD of 51 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 196 = 0 remainder 51 |
| 2 | 196 ÷ 51 = 3 remainder 43 |
| 3 | 51 ÷ 43 = 1 remainder 8 |
| 4 | 43 ÷ 8 = 5 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 147 | 9114 |
| 172 and 135 | 23220 |
| 130 and 168 | 10920 |
| 18 and 180 | 180 |
| 143 and 151 | 21593 |