Least Common Multiple (LCM) of 70 and 188
The least common multiple (LCM) of 70 and 188 is 6580.
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 188?
First, calculate the GCD of 70 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 188 = 0 remainder 70 |
| 2 | 188 ÷ 70 = 2 remainder 48 |
| 3 | 70 ÷ 48 = 1 remainder 22 |
| 4 | 48 ÷ 22 = 2 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 46 | 5934 |
| 122 and 176 | 10736 |
| 61 and 17 | 1037 |
| 180 and 22 | 1980 |
| 79 and 107 | 8453 |