Least Common Multiple (LCM) of 53 and 196
The least common multiple (LCM) of 53 and 196 is 10388.
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 53 and 196?
First, calculate the GCD of 53 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 196 = 0 remainder 53 |
| 2 | 196 ÷ 53 = 3 remainder 37 |
| 3 | 53 ÷ 37 = 1 remainder 16 |
| 4 | 37 ÷ 16 = 2 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 61 | 1342 |
| 66 and 117 | 2574 |
| 143 and 18 | 2574 |
| 139 and 198 | 27522 |
| 184 and 76 | 3496 |