
Least Common Multiple (LCM) of 123 and 16
The least common multiple (LCM) of 123 and 16 is 1968.
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 123 and 16?
First, calculate the GCD of 123 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 123 ÷ 16 = 7 remainder 11 |
2 | 16 ÷ 11 = 1 remainder 5 |
3 | 11 ÷ 5 = 2 remainder 1 |
4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
120 and 42 | 840 |
88 and 158 | 6952 |
26 and 83 | 2158 |
200 and 70 | 1400 |
42 and 22 | 462 |