Least Common Multiple (LCM) of 100 and 36
The least common multiple (LCM) of 100 and 36 is 900.
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 100 and 36?
First, calculate the GCD of 100 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 36 = 2 remainder 28 |
| 2 | 36 ÷ 28 = 1 remainder 8 |
| 3 | 28 ÷ 8 = 3 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 119 | 16422 |
| 144 and 28 | 1008 |
| 151 and 105 | 15855 |
| 122 and 130 | 7930 |
| 29 and 130 | 3770 |