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Sia ? 6 years, 5 months ago
According to question we have to find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
Take the LCM of 20, 25, 35 and 40 i.e.,
20 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 5
25 = 5 {tex}\times{/tex} 5
35 = 1 {tex}\times{/tex} 5 {tex}\times{/tex} 7
40 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 2 {tex}\times{/tex} 5
Now LCM of 20, 25, 35 & 40 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 5 {tex}\times{/tex} 5 {tex}\times{/tex} 7 {tex}\times{/tex} 2 = 1400
If the number 1400 is divided by 20, 25, 35, 40 it leaves a remainder 14, 19, 29, 34.
i.e. 6 less than the divisor in each case
Hence, the required number = 1400 - 6 = 1394.
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