Question
Download Solution PDFFind the greatest number of six digits which is divisible by 25, 35, 42 and 75.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Find the greatest number of six digits which is divisible by 25, 35, 42, and 75.
Formula used:
To find the greatest six-digit number divisible by multiple numbers, calculate the LCM (Least Common Multiple) of the given numbers and divide the largest six-digit number by the LCM. The result is multiplied back by the LCM.
Calculation:
Largest six-digit number = 999999
Given numbers: 25, 35, 42, 75
Find the LCM of 25, 35, 42, and 75
Prime factorization:
25 = 5 × 5
35 = 5 × 7
42 = 2 × 3 × 7
75 = 3 × 5 × 5
LCM = Highest powers of all primes = 2 × 3 × 5 × 5 × 7 = 1050
Divide the largest six-digit number by the LCM
⇒ 999999 ÷ 1050 = 952.380857 (Take the integer part, 952)
Multiply the result by the LCM
⇒ 952 × 1050 = 999600
∴ The correct answer is option 1 (999600).
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