Least Common Multiple (LCM) of 196 and 74
The least common multiple (LCM) of 196 and 74 is 7252.
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 74?
First, calculate the GCD of 196 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 74 = 2 remainder 48 |
| 2 | 74 ÷ 48 = 1 remainder 26 |
| 3 | 48 ÷ 26 = 1 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 54 | 594 |
| 23 and 81 | 1863 |
| 42 and 24 | 168 |
| 196 and 19 | 3724 |
| 22 and 43 | 946 |