Least Common Multiple (LCM) of 100 and 147
The least common multiple (LCM) of 100 and 147 is 14700.
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 147?
First, calculate the GCD of 100 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 147 = 0 remainder 100 |
| 2 | 147 ÷ 100 = 1 remainder 47 |
| 3 | 100 ÷ 47 = 2 remainder 6 |
| 4 | 47 ÷ 6 = 7 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 40 | 1320 |
| 45 and 26 | 1170 |
| 87 and 108 | 3132 |
| 156 and 122 | 9516 |
| 138 and 32 | 2208 |