Least Common Multiple (LCM) of 196 and 42
The least common multiple (LCM) of 196 and 42 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 196 and 42?
First, calculate the GCD of 196 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 42 = 4 remainder 28 |
| 2 | 42 ÷ 28 = 1 remainder 14 |
| 3 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 85 | 12665 |
| 169 and 12 | 2028 |
| 69 and 145 | 10005 |
| 20 and 120 | 120 |
| 169 and 11 | 1859 |