Answer :
Final answer:
The G.C.D of 210 and 525 is 105 and the L.C.M of 210 and 525 is 1050.
Explanation:
The Greatest Common Divisor (G.C.D) of two or more integers is the largest positive integer that divides the numbers without leaving a remainder. To find the G.C.D. of 210 and 525, you would first factorize each value.
The prime factorization of 210 is 2 x 3 x 5 x 7 and for 525 it is 3 x 5 x 5 x 7.
The common factors are 3, 5, and 7.
Multiplying these together, we get 3 x 5 x 7 = 105.
So, the G.C.D of 210 and 525 is 105.
The Least Common Multiple (L.C.M) of two integers is the smallest positive integer that is divisible by both numbers. The L.C.M is found by multiplying all prime factors the highest number of times they occur in either number.
For 210 this would be 2 x 3 x 5 x 7 and for 525 it is 3 x 5 x 5 x 7.
Multiplying all these factors together, we get 2 x 3 x 5 x 5 x 7 = 1050.
So, the LCM of 210 and 525 is 1050.
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