Least Common Multiple (LCM) of 142 and 196
The least common multiple (LCM) of 142 and 196 is 13916.
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 142 and 196?
First, calculate the GCD of 142 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 196 = 0 remainder 142 |
| 2 | 196 ÷ 142 = 1 remainder 54 |
| 3 | 142 ÷ 54 = 2 remainder 34 |
| 4 | 54 ÷ 34 = 1 remainder 20 |
| 5 | 34 ÷ 20 = 1 remainder 14 |
| 6 | 20 ÷ 14 = 1 remainder 6 |
| 7 | 14 ÷ 6 = 2 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 40 | 560 |
| 119 and 60 | 7140 |
| 79 and 96 | 7584 |
| 54 and 192 | 1728 |
| 153 and 16 | 2448 |