What is the least number which when divisible by 2 3 4 5 and 6 leaves remainder 1 in each case but when divided by 7 leaves no remainder A 231 B 301 C 371 D 441?

So, the least number is 301 when divided by 2,3,4,5,6 leaves a remainder 1, but when divided by 7, there will be no remainder.

What is the least common multiple of 4 5 and 7?

140
Answer: LCM of 4, 5, and 7 is 140.

Is there a divisibility rule for 7?

The divisibility rule of 7 states that for a number to be divisible by 7, the last digit of the given number should be multiplied by 2 and then subtracted with the rest of the number leaving the last digit. If the difference is 0 or a multiple of 7, then it is divisible by 7.

What is the least number when divided by 2 3 4 5 6?

The least number when divided by 2, 3, 4, 5 and 6 is leaving 1 as the remainder the number has to be the LCM of 2, 3, 4, 5 and 6 plus 1, which is nothing but 60+1 = 61. Additionally, such a number has to be divisible by 7 and 61 is not the required number. For this, we have to try out the multiples of 60 and add one to it.

What is the LCM of 2 3 4 4 5 6?

Step 1-Find out the LCM of 2, 3, 4, 5, 6 which is 60. Step 2-Add 1 to 60 which is 61. Step 3-Multiple 61 by 7 repeatedly till it fulfills the condition that remainder should be 1.

What is the least common multiple of 3 4 5 and 7?

Since 3,4,5 and 7 are pairwise co-prime their least common multiple is their product: 3*4*5*7 = 420. So if x is a solution to the puzzle, then 420 + x is a solution as well (but a bigger one), and x – 420 is a solution as well (a smaller one). Therefore all the solutions are of the form 420n + 119.

What is the least number that is 60*5+1 = 721?

Thus the least number is 301, meeting all the conditions (7 divides it and leaves remainder of 1 with 2, 3, 4, 5 and 6). The first numbr is 60*5+1 = 300+1, o the next number is 60* (5+7)+1 = 60*12+1 = 721.

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