Least Common Multiple (LCM) of 84 and 55
The least common multiple (LCM) of 84 and 55 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 55?
First, calculate the GCD of 84 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 55 = 1 remainder 29 |
| 2 | 55 ÷ 29 = 1 remainder 26 |
| 3 | 29 ÷ 26 = 1 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 40 | 1080 |
| 158 and 170 | 13430 |
| 143 and 70 | 10010 |
| 26 and 140 | 1820 |
| 62 and 174 | 5394 |