Least Common Multiple (LCM) of 172 and 35
The least common multiple (LCM) of 172 and 35 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 172 and 35?
First, calculate the GCD of 172 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 35 = 4 remainder 32 |
| 2 | 35 ÷ 32 = 1 remainder 3 |
| 3 | 32 ÷ 3 = 10 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 18 | 108 |
| 141 and 46 | 6486 |
| 106 and 191 | 20246 |
| 154 and 84 | 924 |
| 45 and 175 | 1575 |