Find the greatest number of five digits exactly divisible by 9, 12, 15, 18 and 24

Least Common Multiple (LCM)

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. The Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD). As an illustration, LCM (4, 5) = 20. In this case, the LCM 20 can be divided by both 4 and 5, so these two numbers are referred to as the divisors of 20.

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction. The simplification process is facilitated by this procedure.

Properties of LCM

Associative property-LCM(a, b) = LCM(b, a)

Commutative property-LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c))

Distributive property-LCM(da, db, dc) = dLCM(a, b, c)

Summary:

Find the greatest number of 5 digits exactly divisible by 9,12,15,18 and 24.

99720 is the largest sum of five digits that is exactly divisible by 9, 12, 15, 18, and 24. In mathematics, the sum can be defined as the result or answer after adding two or more numbers or terms.

Answer.

LCM of 9, 12, 15, 18 and 24 by division method is 360.
Largest number of five digits = 99999
The quotient when 99999 is divided by 360 is 277 and the remainder is 279.
Greatest number of five digits divisible by 9, 12, 15, 18 and 24 = 99999 - 279 = 99720

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Updated On: 27-06-2022

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Answer : 99720

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