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Finding Common Ground

One table for the HCF and the LCM

Take 126 and 198. Writing both prime lists is slow. One table can give the HCF and the LCM together.

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Start with 126 and 198.
Step 1 of 7
  1. Start with 126 and 198.
  2. Both go into 2. Write 63 and 99 below.
  3. Both go into 3. Write 21 and 33 below.
  4. Both go into 3 again. Write 7 and 11 below.
  5. 7 and 11 are co-prime. Stop here.
  6. HCF: multiply the divisors. 2 × 3 × 3 = 18.
  7. LCM: multiply the divisors and the last row. 18 × 7 × 11 = 1386.

The rule

Look for a prime that goes into both numbers. Divide both by that prime. Write the two answers on a new row. Repeat these steps on the new row. The numbers you divide by are the divisors. The row where you stop is the last row.

Stop when the two numbers in a row are co-prime. Multiply the divisors for the HCF. Multiply the divisors and the last row for the LCM.

Each divisor goes into both numbers. The last row shares nothing. So no bigger common factor is left. The LCM needs the last row too, as it is not shared.

You may divide by a bigger shared factor, such as 6. You still stop at a co-prime row.

Jump to lesson

This track

  1. 0 Start here
  2. 1 The primes inside a number
  3. 2 A factor tree, and where it ends
  4. 3 The biggest one they share
  5. 4 Reading it off the two prime lists
  6. 5 When two step counts meet
  7. 6 The same two lists, read the other way
  8. 7 Which one does the question want?
  9. 8 Check it before you hand it in
  10. 9 Co-prime numbers
  11. 10 One table for the HCF and the LCM
  12. 11 The HCF, the LCM and the product
  13. 12 Checkpoint
  14. 13 The big picture
  15. 14 Track quiz

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