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 |
|---|---|
| 113 and 69 | 7797 |
| 160 and 137 | 21920 |
| 105 and 52 | 5460 |
| 82 and 153 | 12546 |
| 49 and 176 | 8624 |