Least Common Multiple (LCM) of 84 and 117
The least common multiple (LCM) of 84 and 117 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 84 and 117?
First, calculate the GCD of 84 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 117 = 0 remainder 84 |
| 2 | 117 ÷ 84 = 1 remainder 33 |
| 3 | 84 ÷ 33 = 2 remainder 18 |
| 4 | 33 ÷ 18 = 1 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 92 | 3772 |
| 110 and 111 | 12210 |
| 69 and 36 | 828 |
| 137 and 107 | 14659 |
| 85 and 19 | 1615 |