Eggs in basket

If the eggs in a basket are removed twice at a time, one will remain. Two eggs will remain if the eggs are removed three at a time. If the eggs are removed four, five, or six at a time, the three, four, and five eggs will remain, respectively. However, no eggs will be left over if they are taken out seven at a time.
Find the smallest number of eggs that could be in the basket.

Correct answer:

n =  119

Step-by-step explanation:

n=2x+1 n=3y+2 n=4z+3 n=5w+4 n=6q+5 n=7k  2 ...  prime number 3 ...  prime number 4=22 5 ...  prime number 6=23 LCM(2,3,4,5,6)=2235=60  z1=LCM(2,3,4,5,6)=60 t1=(1 z11)/7=(1 601)/7=759=8738.4286 t2=(2 z11)/7=(2 601)/7=17 t3=(3 z11)/7=(3 601)/7=7179=257425.5714 t4=(4 z11)/7=(4 601)/7=7239=347134.1429 t5=(5 z11)/7=(5 601)/7=7299=427542.7143   n=2 z11=2 601=119   Verifying Solution:  119 = 2 × 59 + 1 119 = 3 × 39 + 2 119 = 4 × 29 + 3 119 = 5 × 23 + 4 119 = 6 × 19 + 5 119 = 7 × 17



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