Least Common Multiple (LCM) of 117 and 16
The least common multiple (LCM) of 117 and 16 is 1872.
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 16?
First, calculate the GCD of 117 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 16 = 7 remainder 5 |
| 2 | 16 ÷ 5 = 3 remainder 1 |
| 3 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 96 | 17760 |
| 83 and 41 | 3403 |
| 69 and 56 | 3864 |
| 35 and 113 | 3955 |
| 113 and 16 | 1808 |