Least Common Multiple (LCM) of 51 and 97
The least common multiple (LCM) of 51 and 97 is 4947.
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 97?
First, calculate the GCD of 51 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 97 = 0 remainder 51 |
| 2 | 97 ÷ 51 = 1 remainder 46 |
| 3 | 51 ÷ 46 = 1 remainder 5 |
| 4 | 46 ÷ 5 = 9 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 108 | 6372 |
| 125 and 35 | 875 |
| 59 and 94 | 5546 |
| 103 and 199 | 20497 |
| 123 and 100 | 12300 |