Least Common Multiple (LCM) of 180 and 35
The least common multiple (LCM) of 180 and 35 is 1260.
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 180 and 35?
First, calculate the GCD of 180 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 35 = 5 remainder 5 |
| 2 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 58 | 9338 |
| 151 and 135 | 20385 |
| 170 and 106 | 9010 |
| 55 and 73 | 4015 |
| 21 and 128 | 2688 |