Least Common Multiple (LCM) of 143 and 90
The least common multiple (LCM) of 143 and 90 is 12870.
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 143 and 90?
First, calculate the GCD of 143 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 90 = 1 remainder 53 |
| 2 | 90 ÷ 53 = 1 remainder 37 |
| 3 | 53 ÷ 37 = 1 remainder 16 |
| 4 | 37 ÷ 16 = 2 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 22 | 1122 |
| 130 and 198 | 12870 |
| 111 and 97 | 10767 |
| 110 and 111 | 12210 |
| 132 and 113 | 14916 |