What is the least common denominator for 15, 18, 25 ?

Question

LCD for 15, 18, 25

Answer 1

Another method - perhaps a simpler one to understand is as follows

 

Find prime factors of first number which is the LCM = 15 = 3 * 5

Find LCM of  the previous LCM and the new number which just includes the prime factors(repeated if needed) and 

LCM of 15(3*5) and 18(3*3*2) = LCM pf previous(3*5 and 3*3*2)= 3*5*3*2 =90 or(2*3*3*5) - note the 3 needs to be repeated since it does not appear twice in the previous LCM(15)

 

Repeat the above steps with the remaining numbers until done

 

LCM of 90(2*3*3*5) and 25(5*5) which is (2*3*3*5*5) = 450

 

Note when the prime factors contains a repetition of at least the same number of factors such as 5,5 in 25 the LCM must also include two 5s

e.g. LCM(25 and 5) is LCM( 5*5 and 5) = 5*5. It wont' be just 5

Answer 2

One method for finding the Least Common Multiple (which is used as the Least Common Denominator) is to list the multiples of each number, then identify the least (lowest common number).

 

For 15: 15 30 45 60 ... 225 240 255 270 285 300 315 330 345 360 375 390 405 420 435 450 465 480
For 18: 18 36 54 72 ... 270 288 306 324 342 360 378 396 414 432 450 468 486 504 522 540 558 576
For 25: 25 50 75 100 ...375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800

 

Another method is to list the prime factors of each number, then find the superset that includes each set of factors:

 

For 15:  3 * 5

For 18:  2 * 3 * 3

For 25:  5 * 5

 

    The superset that includes these three sets is  2 * 3 * 3 * 5 *5 = 450

 

Now, be sure to multiply the numerator by the appropriate value also.