Question

find the smallest natural number which when divided by 18 35 36 and 70 leaves remainder 7 in each case

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Answer 1

First, find the LCM of the given numbers :

18 = 2*3*3

35 = 5*7

36 = 2*3*3*2 = 18*2

70 = 2*5*7 = 35*2

Taking LCM of 36 and 70 as they are multiples of 18,35

LCM = 2*3*3*2*5*7 = 2520  

2520 can be divided completely by 18,35,36 and 70

To get remainder = 7,

Simply add 7 to the LCM

= 2520 + 7  = 2527

Answer 2

Step-by-step explanation:

$The \: smallest \: number \: which \: when \: divided \: by 18,\:35 \: ,36\: and \: 70 = LCM(18 \: 35,36,70)</p><p></p><p></p><p>35=5×7</p><p></p><p>56=23×7</p><p></p><p>91=7×13 \: </p><p></p><p></p><p>LCM=23×5×7×13=3640 \: </p><p></p><p></p><p>The smallest number that when divided by 13 \: 35, 36, \: 70</p><p></p><p>$