Least Common Multiple (LCM) of 84 and 145
The least common multiple (LCM) of 84 and 145 is 12180.
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 145?
First, calculate the GCD of 84 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 145 = 0 remainder 84 |
| 2 | 145 ÷ 84 = 1 remainder 61 |
| 3 | 84 ÷ 61 = 1 remainder 23 |
| 4 | 61 ÷ 23 = 2 remainder 15 |
| 5 | 23 ÷ 15 = 1 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 75 | 12675 |
| 21 and 60 | 420 |
| 11 and 54 | 594 |
| 146 and 91 | 13286 |
| 22 and 190 | 2090 |