Find The Greatest 4 Digit Number Exactly Divisible By 3 4 And 5 Here is a step by step procedure to find the greatest four digit number that is exactly divisible by 18,24,36. find the lcm (least common multiple) of 18, 24, 36. any number divisible by the lcm of the 18,24,36 will be divisible by each of 18,24,36. to find lcm, write each number as a product of its prime factors. The greatest four digit number = 9999. we can get the required number by following steps: step 1 : divide 9999 by lcm of 15, 24 and 36. step 2 : subtract result of step 1 from 9999. prime factorization : 15 = 3 × 5. 24 = 2 3 × 3. 36 = 2 2 × 3 2. lcm (15, 24, 36) = 2 3 × 3 2 × 5 = 360.
Example 11 Find The Greatest 4 Digit Number Which Is A Perfect A number is divisible by 15 = 3 × 5 if and only if it is divisible by 3 and 5. a number is divisible by 18 = 2 × 3² if and only if it is divisible by 2 and 9. a number is divisible by 20 = 2² × 5 if and only if it is divisible by 4 and by 5. simple — automatic even — but less and less useful, right? however, sometimes we can rephrase. "find the largest $4$ digit number that is exactly divisible by $12,15,18$ and $27$." if all those number divide into that 4 digit number than that 4 digit number is a multiple of all those numbers. so the 4 digit number is a common multiple of all of those. "the solution is by finding out the lcm of these numbers. i mean why ?". The greatest 4 digit number is 9999. now, find the lcm of 40, 48 and 60. divide 9999 by 4 so that we get the remainder, remainder is 3. now, subtract the remainder from 9999. therefore, the required number is 9996 which is exactly divisible by 40, 48 and 60. advertisement. If any number n is divisible by a set of numbers a, b, c then the l.c.m. of a, b, and c also divides the number n. calculation: the greatest 4 digit number is 9999.
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