Prime Time – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash, tailored for Class 6 in Mathematics.
This one-pager compiles key formulas and equations from the Prime Time chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
LCM(a, b) = (a × b) / GCD(a, b)
LCM is the least common multiple of two numbers a and b. GCD is the greatest common divisor. This formula helps find the LCM using the GCD.
GCD(a, b) × LCM(a, b) = a × b
This relationship indicates that the product of GCD and LCM of two numbers equals the product of the numbers. It connects the two concepts and aids in calculations.
Multiple of a number: n × k
Where n is the base number and k is any positive integer. This formula generates the multiples of n (e.g., 3 × 1 = 3, 3 × 2 = 6). Useful in games like Idli-Vada.
Common multiple: LCM(n1, n2)
The smallest number that is a multiple of both n1 and n2. Useful for identifying numbers in games involving multiples.
Divisibility rule for 3: sum of digits divisible by 3
A number is divisible by 3 if the sum of its digits is divisible by 3 (e.g., in 123, 1+2+3=6, which is divisible by 3).
Divisibility rule for 5: last digit is 0 or 5
A number is divisible by 5 if its last digit is 0 or 5 (e.g., 25 is divisible because its last digit is 5).
Divisibility rule for 15: divisible by both 3 and 5
A number is divisible by 15 if it meets the criteria for both 3 and 5. This is useful in determining ‘idli-vada’ outcomes.
Sum of first n natural numbers: S = n(n + 1)/2
Where S is the sum and n is the last number in the series. This formula calculates the total of a consecutive number series.
Square of a number: n²
Where n is any integer. The square represents the area of a square with side n. Useful for geometric calculations.
Area of a rectangle: A = l × w
Where A is area, l is length, and w is width. This formula is crucial in practical applications like calculating space.
Equations
3 × k = {3, 6, 9, 12, ...}
This represents the multiples of 3, where k is any positive integer. Players say 'idli' when they reach these numbers.
5 × k = {5, 10, 15, 20, ...}
This represents the multiples of 5, where k is any positive integer. Players say 'vada' for these numbers.
If n % 3 == 0 then say ‘idli’
This condition checks if n is divisible by 3. If true, players must say 'idli' instead of the number.
If n % 5 == 0 then say ‘vada’
This condition checks if n is divisible by 5. If true, players must say 'vada' instead of the number.
If n % 15 == 0 then say ‘idli-vada’
This condition checks if n is divisible by both 3 and 5. If true, players must say 'idli-vada'.
Count of multiples of 3 ≤ N: floor(N/3)
Use this formula to find how many multiples of 3 exist up to N. Useful in calculating outcomes.
Count of multiples of 5 ≤ N: floor(N/5)
Use this to find how many multiples of 5 exist up to N. Aids in game strategy.
Count of multiples of 15 ≤ N: floor(N/15)
This is used to find how many commonly divisible numbers (idli-vada) exist ≤ N.
Final player out count = Total players - mistakes
This calculates how many players remain after mistakes. Helps analyze game outcomes.
Game duration: t = n / (players count)
Where t is the time taken, n is the total number spoken. This can illustrate game dynamics.
