Least Common Multiple (LCM) of 196 and 35
The least common multiple (LCM) of 196 and 35 is 980.
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 35?
First, calculate the GCD of 196 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 35 = 5 remainder 21 |
| 2 | 35 ÷ 21 = 1 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 199 | 38606 |
| 76 and 112 | 2128 |
| 55 and 110 | 110 |
| 22 and 31 | 682 |
| 180 and 173 | 31140 |