Least Common Multiple (LCM) of 90 and 152
The least common multiple (LCM) of 90 and 152 is 6840.
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 152?
First, calculate the GCD of 90 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 152 = 0 remainder 90 |
| 2 | 152 ÷ 90 = 1 remainder 62 |
| 3 | 90 ÷ 62 = 1 remainder 28 |
| 4 | 62 ÷ 28 = 2 remainder 6 |
| 5 | 28 ÷ 6 = 4 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 117 | 12402 |
| 136 and 10 | 680 |
| 171 and 18 | 342 |
| 183 and 162 | 9882 |
| 181 and 106 | 19186 |