# Problems from Greatest common divisor and Least common multiple

Find the greatest common divisor of the following sets of numbers: $$(34, 25), (80, 45), (66, 52, 70)$$.

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### Development:

$$34=2\times17, \ \ \ \ 25=5^2$$

$$g.c.d.(34,25)=1$$ (They do not have common divisors but $$1$$.)

$$80=2^4\times5, \ \ \ \ 45=3^2\times5$$

$$g.c.d(80,45)=5$$

$$66=2\times3\times11, \ \ \ \ 52=2^2\times13, \ \ \ \ 70=2\times5\times6$$

$$g.c.d.(66,52,70)=2$$

### Solution:

$$g.c.d. (34,25) = 1 \\ g.c.d. (80,45) = 5 \\ g.c.d. (66,52,70) = 2$$

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Find the least common multiple of the following sets of numbers: $$(49, 33), (56, 100, 24), (72, 41, 16)$$.

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### Development:

$$49=7^2, \ \ \ \ 33=3\times11$$

$$l.c.m.(49,33)=3\times7^2\times11=1617$$

$$56=2^3\times7, \ \ \ \ 100=2^2\times5^2, \ \ \ \ 24=2^3\times3$$

$$l.c.m.(56,100,24)=2^3\times3\times5^2\times7=4200$$

$$72=2^3\times3^2, \ \ \ \ 41=41\times1, \ \ \ \ 16=2^4$$

$$l.c.m.(72,41,16)=2^4\times3^2\times41=5904$$

### Solution:

$$l.c.m. (49,39) = 1617 \\ l.c.m. (56,100,24) = 4200 \\ l.c.m. (72,41,16) = 5904$$

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