Least Common Multiple (LCM) of 74 and 196
The least common multiple (LCM) of 74 and 196 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 74 and 196?
First, calculate the GCD of 74 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 196 = 0 remainder 74 |
| 2 | 196 ÷ 74 = 2 remainder 48 |
| 3 | 74 ÷ 48 = 1 remainder 26 |
| 4 | 48 ÷ 26 = 1 remainder 22 |
| 5 | 26 ÷ 22 = 1 remainder 4 |
| 6 | 22 ÷ 4 = 5 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 174 | 3828 |
| 178 and 93 | 16554 |
| 103 and 187 | 19261 |
| 31 and 133 | 4123 |
| 104 and 60 | 1560 |