Least Common Multiple (LCM) of 84 and 110
The least common multiple (LCM) of 84 and 110 is 4620.
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 110?
First, calculate the GCD of 84 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 110 = 0 remainder 84 |
| 2 | 110 ÷ 84 = 1 remainder 26 |
| 3 | 84 ÷ 26 = 3 remainder 6 |
| 4 | 26 ÷ 6 = 4 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 199 | 35820 |
| 117 and 147 | 5733 |
| 101 and 135 | 13635 |
| 132 and 107 | 14124 |
| 169 and 185 | 31265 |