Least Common Multiple (LCM) of 84 and 143
The least common multiple (LCM) of 84 and 143 is 12012.
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 143?
First, calculate the GCD of 84 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 143 = 0 remainder 84 |
| 2 | 143 ÷ 84 = 1 remainder 59 |
| 3 | 84 ÷ 59 = 1 remainder 25 |
| 4 | 59 ÷ 25 = 2 remainder 9 |
| 5 | 25 ÷ 9 = 2 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 175 | 2450 |
| 110 and 117 | 12870 |
| 197 and 37 | 7289 |
| 12 and 119 | 1428 |
| 55 and 127 | 6985 |