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The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
- a)9000
- b)9400
- c)9600
- d)9800
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The greatest number of four digits which is divisible by 15, 25, 40 an...
To find the greatest number of four digits which is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers.
1. Finding the LCM of 15 and 25:
To find the LCM of 15 and 25, we need to find the prime factors of both numbers.
Prime factors of 15: 3, 5
Prime factors of 25: 5, 5
The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 15 and 25 is 3 * 5 * 5 = 75.
2. Finding the LCM of 75 and 40:
To find the LCM of 75 and 40, we need to find the prime factors of both numbers.
Prime factors of 75: 3, 5, 5
Prime factors of 40: 2, 2, 2, 5
The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 75 and 40 is 2 * 2 * 2 * 3 * 5 * 5 = 600.
3. Finding the LCM of 600 and 1000:
To find the LCM of 600 and 1000, we need to find the prime factors of both numbers.
Prime factors of 600: 2, 2, 2, 3, 5, 5
Prime factors of 1000: 2, 2, 2, 5, 5, 5
The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 600 and 1000 is 2 * 2 * 2 * 3 * 5 * 5 * 5 = 6000.
Since we are looking for the greatest number of four digits, we need to find the highest multiple of 6000 that is less than 10000.
The greatest multiple of 6000 less than 10000 is 9600. Therefore, the correct option is c) 9600.
1. Finding the LCM of 15 and 25:
To find the LCM of 15 and 25, we need to find the prime factors of both numbers.
Prime factors of 15: 3, 5
Prime factors of 25: 5, 5
The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 15 and 25 is 3 * 5 * 5 = 75.
2. Finding the LCM of 75 and 40:
To find the LCM of 75 and 40, we need to find the prime factors of both numbers.
Prime factors of 75: 3, 5, 5
Prime factors of 40: 2, 2, 2, 5
The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 75 and 40 is 2 * 2 * 2 * 3 * 5 * 5 = 600.
3. Finding the LCM of 600 and 1000:
To find the LCM of 600 and 1000, we need to find the prime factors of both numbers.
Prime factors of 600: 2, 2, 2, 3, 5, 5
Prime factors of 1000: 2, 2, 2, 5, 5, 5
The LCM is the product of the highest powers of all the prime factors involved. Therefore, the LCM of 600 and 1000 is 2 * 2 * 2 * 3 * 5 * 5 * 5 = 6000.
Since we are looking for the greatest number of four digits, we need to find the highest multiple of 6000 that is less than 10000.
The greatest multiple of 6000 less than 10000 is 9600. Therefore, the correct option is c) 9600.
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Community Answer
The greatest number of four digits which is divisible by 15, 25, 40 an...
Greatest number of 4-digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600. On dividing 9999 by 600, the remainder is 399. Required number (9999 - 399) = 9600.
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The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:a)9000 b)9400 c)9600 d)9800Correct answer is option 'C'. Can you explain this answer?
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