Multiple and remainder

What is the least multiple of 7, which, when divided by each one of 6,9,15,18, gives the remainder of 4 in each case?

Correct answer:

n =  364

Step-by-step explanation:

6=23 9=32 15=35 18=232 LCM(6,9,15,18)=2325=90  l=LCM(6,9,15,18)=90  a = (l+4)/7  a1=(1 l+4)/7=(1 90+4)/7=794=137313.4286 a2=(2 l+4)/7=(2 90+4)/7=7184=267226.2857 a3=(3 l+4)/7=(3 90+4)/7=7274=397139.1429 a4=(4 l+4)/7=(4 90+4)/7=52  n=4 l+4=4 90+4=364   Verifying Solution:  364 = 2 × 2 × 7 × 13 = 22 × 7 × 13 d1=n/7=364/7=52 364 = 7 × 52 + 0 364 = 6 × 60 + 4 364 = 9 × 40 + 4 364 = 15 × 24 + 4 364 = 18 × 20 + 4



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