Least Common Multiple (LCM) of 61 and 90
The least common multiple (LCM) of 61 and 90 is 5490.
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 61 and 90?
First, calculate the GCD of 61 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 90 = 0 remainder 61 |
| 2 | 90 ÷ 61 = 1 remainder 29 |
| 3 | 61 ÷ 29 = 2 remainder 3 |
| 4 | 29 ÷ 3 = 9 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 148 | 5624 |
| 184 and 124 | 5704 |
| 60 and 75 | 300 |
| 128 and 196 | 6272 |
| 70 and 120 | 840 |