Least Common Multiple (LCM) of 67 and 90
The least common multiple (LCM) of 67 and 90 is 6030.
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 67 and 90?
First, calculate the GCD of 67 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 90 = 0 remainder 67 |
| 2 | 90 ÷ 67 = 1 remainder 23 |
| 3 | 67 ÷ 23 = 2 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 29 | 1363 |
| 74 and 60 | 2220 |
| 62 and 35 | 2170 |
| 18 and 128 | 1152 |
| 66 and 54 | 594 |