Least Common Multiple (LCM) of 196 and 76
The least common multiple (LCM) of 196 and 76 is 3724.
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 76?
First, calculate the GCD of 196 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 76 = 2 remainder 44 |
| 2 | 76 ÷ 44 = 1 remainder 32 |
| 3 | 44 ÷ 32 = 1 remainder 12 |
| 4 | 32 ÷ 12 = 2 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 52 | 260 |
| 48 and 107 | 5136 |
| 193 and 160 | 30880 |
| 66 and 140 | 4620 |
| 134 and 165 | 22110 |