Least Common Multiple (LCM) of 65 and 98
The least common multiple (LCM) of 65 and 98 is 6370.
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 65 and 98?
First, calculate the GCD of 65 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 98 = 0 remainder 65 |
| 2 | 98 ÷ 65 = 1 remainder 33 |
| 3 | 65 ÷ 33 = 1 remainder 32 |
| 4 | 33 ÷ 32 = 1 remainder 1 |
| 5 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 21 | 336 |
| 150 and 36 | 900 |
| 142 and 193 | 27406 |
| 10 and 58 | 290 |
| 151 and 62 | 9362 |