Least Common Multiple (LCM) of 85 and 132
The least common multiple (LCM) of 85 and 132 is 11220.
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 85 and 132?
First, calculate the GCD of 85 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 132 = 0 remainder 85 |
| 2 | 132 ÷ 85 = 1 remainder 47 |
| 3 | 85 ÷ 47 = 1 remainder 38 |
| 4 | 47 ÷ 38 = 1 remainder 9 |
| 5 | 38 ÷ 9 = 4 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 137 | 9590 |
| 125 and 117 | 14625 |
| 168 and 120 | 840 |
| 11 and 148 | 1628 |
| 153 and 54 | 918 |