Least Common Multiple (LCM) of 76 and 196
The least common multiple (LCM) of 76 and 196 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 76 and 196?
First, calculate the GCD of 76 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 196 = 0 remainder 76 |
| 2 | 196 ÷ 76 = 2 remainder 44 |
| 3 | 76 ÷ 44 = 1 remainder 32 |
| 4 | 44 ÷ 32 = 1 remainder 12 |
| 5 | 32 ÷ 12 = 2 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 88 | 8536 |
| 171 and 121 | 20691 |
| 96 and 20 | 480 |
| 31 and 129 | 3999 |
| 30 and 101 | 3030 |