Least Common Multiple (LCM) of 36 and 175
The least common multiple (LCM) of 36 and 175 is 6300.
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 36 and 175?
First, calculate the GCD of 36 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 175 = 0 remainder 36 |
| 2 | 175 ÷ 36 = 4 remainder 31 |
| 3 | 36 ÷ 31 = 1 remainder 5 |
| 4 | 31 ÷ 5 = 6 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 144 | 1008 |
| 53 and 174 | 9222 |
| 165 and 95 | 3135 |
| 157 and 157 | 157 |
| 37 and 137 | 5069 |