LCM for 17 and 45

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What's the Least Common Multiple (LCM) of 17 and 45?

Answer

LCM of 17 and 45 is
765

First common multiples: 765; 1,530; 2,295; …

765 is divisible by both: 765 ÷ 17 = 45, 765 ÷ 45 = 17 — and 45 and 17 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/17 by 45 and of y/45 by 17.

17 and 45 are coprime (GCF = 1), so their LCM is simply the product: 17 × 45 = 765.

17 — prime

45 = 32 × 5

Prime1745Highest power
3—3232
5—55
1717—17

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 32 × 5 × 17 = 765

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LCM Table

Number 1Number 2LCM
1718306
1719323
1720340
1724408
1725425
1727459
1728476
1729493
1731527
173434
1735595
1741697
1742714
1744748
1745765
1746782
1749833
175151
1752884
1754918
17591,003

FAQ

What's the Least Common Multiple (LCM) of 17 and 45?

LCM of 17 and 45 is 765

How to find the LCM of 17 and 45 using prime factorization?

To find the LCM of 17 and 45, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 765.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 17 and 45: LCM = 765, GCF = 1.

See Also