Least Common Multiple (LCM) of 100 and 196
The least common multiple (LCM) of 100 and 196 is 4900.
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 100 and 196?
First, calculate the GCD of 100 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 196 = 0 remainder 100 |
| 2 | 196 ÷ 100 = 1 remainder 96 |
| 3 | 100 ÷ 96 = 1 remainder 4 |
| 4 | 96 ÷ 4 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 195 | 11310 |
| 157 and 164 | 25748 |
| 89 and 140 | 12460 |
| 25 and 169 | 4225 |
| 13 and 100 | 1300 |