Least Common Multiple (LCM) of 196 and 90
The least common multiple (LCM) of 196 and 90 is 8820.
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 90?
First, calculate the GCD of 196 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 90 = 2 remainder 16 |
| 2 | 90 ÷ 16 = 5 remainder 10 |
| 3 | 16 ÷ 10 = 1 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 130 | 650 |
| 77 and 69 | 5313 |
| 67 and 55 | 3685 |
| 116 and 197 | 22852 |
| 95 and 111 | 10545 |