Least Common Multiple (LCM) of 42 and 196
The least common multiple (LCM) of 42 and 196 is 588.
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 42 and 196?
First, calculate the GCD of 42 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 196 = 0 remainder 42 |
| 2 | 196 ÷ 42 = 4 remainder 28 |
| 3 | 42 ÷ 28 = 1 remainder 14 |
| 4 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 91 | 9737 |
| 30 and 38 | 570 |
| 116 and 54 | 3132 |
| 143 and 155 | 22165 |
| 80 and 192 | 960 |