Least Common Multiple (LCM) of 117 and 98
The least common multiple (LCM) of 117 and 98 is 11466.
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 117 and 98?
First, calculate the GCD of 117 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 98 = 1 remainder 19 |
| 2 | 98 ÷ 19 = 5 remainder 3 |
| 3 | 19 ÷ 3 = 6 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 63 | 756 |
| 165 and 75 | 825 |
| 104 and 19 | 1976 |
| 46 and 72 | 1656 |
| 158 and 70 | 5530 |