Least Common Multiple (LCM) of 84 and 142
The least common multiple (LCM) of 84 and 142 is 5964.
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 142?
First, calculate the GCD of 84 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 142 = 0 remainder 84 |
| 2 | 142 ÷ 84 = 1 remainder 58 |
| 3 | 84 ÷ 58 = 1 remainder 26 |
| 4 | 58 ÷ 26 = 2 remainder 6 |
| 5 | 26 ÷ 6 = 4 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 33 | 1716 |
| 45 and 23 | 1035 |
| 144 and 114 | 2736 |
| 168 and 86 | 7224 |
| 92 and 14 | 644 |