Least Common Multiple (LCM) of 60 and 90
The least common multiple (LCM) of 60 and 90 is 180.
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 60 and 90?
First, calculate the GCD of 60 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 90 = 0 remainder 60 |
| 2 | 90 ÷ 60 = 1 remainder 30 |
| 3 | 60 ÷ 30 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 111 | 1554 |
| 117 and 131 | 15327 |
| 195 and 71 | 13845 |
| 162 and 90 | 810 |
| 106 and 59 | 6254 |