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 |
|---|---|
| 67 and 128 | 8576 |
| 157 and 178 | 27946 |
| 141 and 127 | 17907 |
| 53 and 21 | 1113 |
| 60 and 13 | 780 |