Question

find find the LCM and HCF of 43263 and 15295 by applying the fundamental theorem of arithmetic method

Answer 1

Step 1. Divide the larger number by the smaller one:
43,263 ÷ 15,295 = 2 + 12,673;
Step 2. Divide the smaller number by the above operation's remainder:
15,295 ÷ 12,673 = 1 + 2,622;
Step 3. Divide the remainder from the step 1 by the remainder from the step 2:
12,673 ÷ 2,622 = 4 + 2,185;
Step 4. Divide the remainder from the step 2 by the remainder from the step 3:
2,622 ÷ 2,185 = 1 + 437;
Step 5. Divide the remainder from the step 3 by the remainder from the step 4:
2,185 ÷ 437 = 5 + 0;
At this step, the remainder is zero, so we stop:
437 is the number we were looking for, the last remainder that is not zero.
This is the greatest common factor (divisor).
Least common multiple, lcm:
lcm (a; b) = (a × b) / gcf, gcd (a; b);
lcm (43,263; 15,295) = (43,263 × 15,295) / gcf, gcd (43,263; 15,295) = 661,707,585 / 437 = 1,514,205;
Least common multiple
lcm (43,263; 15,295) = 1,514,205 = 32 × 5 × 7 × 11 × 19 × 23;

Answer 2

Here, 43263>15295.So,
43263=15295*2+11673
15295=11673*1+3622
11673=3622*3+807
3622=807*4+394
807=394*2+19
394=19*26+10
19=10*1+9
10=9*1+1
9=1*9+0
so, H. C. F. (43263,15295)=1