Least Common Multiple (LCM) of 90 and 156
The least common multiple (LCM) of 90 and 156 is 2340.
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 156?
First, calculate the GCD of 90 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 156 = 0 remainder 90 |
| 2 | 156 ÷ 90 = 1 remainder 66 |
| 3 | 90 ÷ 66 = 1 remainder 24 |
| 4 | 66 ÷ 24 = 2 remainder 18 |
| 5 | 24 ÷ 18 = 1 remainder 6 |
| 6 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 13 | 1898 |
| 115 and 182 | 20930 |
| 75 and 118 | 8850 |
| 188 and 150 | 14100 |
| 102 and 165 | 5610 |