Least Common Multiple (LCM) of 70 and 172
The least common multiple (LCM) of 70 and 172 is 6020.
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 172?
First, calculate the GCD of 70 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 172 = 0 remainder 70 |
| 2 | 172 ÷ 70 = 2 remainder 32 |
| 3 | 70 ÷ 32 = 2 remainder 6 |
| 4 | 32 ÷ 6 = 5 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 134 | 21038 |
| 184 and 192 | 4416 |
| 119 and 112 | 1904 |
| 142 and 145 | 20590 |
| 176 and 194 | 17072 |