Find the least number which when divided by 25 45 60 leaves a remainder to 20

Question

Mathematics

Karley Bartlett

26 May, 18:36

Find the least number which when divided by 25 45 60 leaves a remainder to 20

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Answers (1)

Know the Answer?

Jaden West · Answer 1

Answer:a=920

Step-by-step explanation: X : Y = Z (R); Z< Y

a : 25 = x (r=20); 20
a:45 = y (r=20); 20
a:60=z (r = 20); 20
a=25x+20 (1)

a=45y+20 (2)

a=60z+20 (3)

(1); (2); (3) ⇒a-20 ∈ [25,45, 60]

25=5²

45=3²x 5

60=2²x 3 x 5

[25, 45, 60]=2²x 3² x 5²=900⇒

⇒a-20∈{0, 900, 1800, ..., 900K}/+20

a ∈ {20, 920, 1820, ..., 920K}

a=920

920: 25=36 (r=20) - True=>

a=920 is the smallest number that divided by 25, 45, 60 leaves a remainder of 20