Question

ज्या संख्येला 2, 3, 4, 5, 6 आणि 7 या संख्यांनी भागले असता बाकी अनुक्रमे 1, 2, 3, 4, 5 आणि 6 उरते अशी सर्वांत लहान संख्या कोणती?

Answer 1

Given :  ज्या संख्येला 2, 3, 4, 5, 6 आणि 7 या संख्यांनी भागले असता बाकी अनुक्रमे 1, 2, 3, 4, 5 आणि 6 उरते

To find :  अशी सर्वांत लहान संख्या कोणती

Solution:

N = 2a + 1 = 2a  + 2 - 1 = 2(a + 1) - 1

N = 3b + 2  = 3b + 3 - 1 = 3(b + 1) - 1

N = 4c + 3  = 4c + 4 - 1 = 4(c + 1) - 1

N = 5d + 4 =  5d + 5 - 1 = 5(d + 1) - 1

N = 6e + 5 = 6e + 6 - 1 = 6(e + 1) - 1

N = 7f + 6  = 7f + 7 - 1 =  7 (f + 1) - 1

=> 2(a + 1)  = 3(b + 1) =  4(c + 1) = 5(d + 1) = 6(e + 1) = 7 (f + 1)  = N + 1

=> N + 1  =   LCM of 2 , 3  4 , 5 , 6 , 7

=> N + 1= 420

N = 419

419 = 2 * 248 + 1

419 = 3 * 139 + 2

419  = 4 * 104 + 3

419 = 5 * 84  + 4

419 = 6 * 69  + 5

419 = 7 * 59 + 6

अशी सर्वात लहान संख्या  = 419

419   is smallest such number

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