Least Common Multiple (LCM) of 90 and 147
The least common multiple (LCM) of 90 and 147 is 4410.
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 90 and 147?
First, calculate the GCD of 90 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 147 = 0 remainder 90 |
| 2 | 147 ÷ 90 = 1 remainder 57 |
| 3 | 90 ÷ 57 = 1 remainder 33 |
| 4 | 57 ÷ 33 = 1 remainder 24 |
| 5 | 33 ÷ 24 = 1 remainder 9 |
| 6 | 24 ÷ 9 = 2 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 178 | 11926 |
| 169 and 27 | 4563 |
| 170 and 74 | 6290 |
| 120 and 15 | 120 |
| 155 and 156 | 24180 |