Smallest whole number divisible by 720 and 1575
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720 divisible by 2 and 1575 is divisible by 3
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5
Given:
720 and 1575.
To find:
The smallest whole number that will divide both the given numbers.
Note:
The smallest whole number that will divide both the numbers is their HCF.
Solution:
HCF of 720 and 1575.
a = 1575 and b = 720.
writing in the form of a = bq + r, we get,
1575 = 720 * 2 + 135
720 = 135 * 5 + 45
135 = 45 * 3 + 0
Conclusion:
Since r = 0, Therefore 45 is the HCF i.e the smallest whole number divisible by both 720 and 1575.
Extra Information:
The above done method is called as Euclid's division lemma or Division algorithm which is used to find HCF or smallest divisible whole number of given numbers.
Euclid's division lemma:
Given positive integers a and b, there exists unique pair of integers q and r satisfying a = bq + r where 0 ≤ r < b.
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