Least Common Multiple (LCM) of 84 and 116
The least common multiple (LCM) of 84 and 116 is 2436.
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 116?
First, calculate the GCD of 84 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 116 = 0 remainder 84 |
| 2 | 116 ÷ 84 = 1 remainder 32 |
| 3 | 84 ÷ 32 = 2 remainder 20 |
| 4 | 32 ÷ 20 = 1 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 195 | 1560 |
| 87 and 147 | 4263 |
| 167 and 143 | 23881 |
| 160 and 175 | 5600 |
| 153 and 81 | 1377 |