Least Common Multiple (LCM) of 70 and 198
The least common multiple (LCM) of 70 and 198 is 6930.
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 70 and 198?
First, calculate the GCD of 70 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 198 = 0 remainder 70 |
| 2 | 198 ÷ 70 = 2 remainder 58 |
| 3 | 70 ÷ 58 = 1 remainder 12 |
| 4 | 58 ÷ 12 = 4 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 108 | 5076 |
| 133 and 48 | 6384 |
| 179 and 89 | 15931 |
| 76 and 63 | 4788 |
| 68 and 70 | 2380 |