Least Common Multiple (LCM) of 117 and 28
The least common multiple (LCM) of 117 and 28 is 3276.
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 28?
First, calculate the GCD of 117 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 28 = 4 remainder 5 |
| 2 | 28 ÷ 5 = 5 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 117 | 12753 |
| 101 and 69 | 6969 |
| 52 and 30 | 780 |
| 124 and 24 | 744 |
| 194 and 200 | 19400 |